{
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  "metadata": {
    "colab": {
      "provenance": [],
      "machine_shape": "hm",
      "toc_visible": true,
      "mount_file_id": "https://github.com/isa-ulisboa/greends-pml/blob/main/ML_overview_with_examples.ipynb",
      "authorship_tag": "ABX9TyMbNPVGp+SkzOvklx3rD1D3",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/isa-ulisboa/greends-pml/blob/main/ML_overview_with_examples.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Practical Machine Learning**\n",
        "\n",
        "Masters in Green Data Science, ISA/ULisboa, 2023-2024\n",
        "\n",
        "Instructor: Manuel Campagnolo mlc@isa.ulisboa.pt"
      ],
      "metadata": {
        "id": "f0qoqpJ4-iom"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Overview of Machine Learning (ML)\n",
        "\n",
        "In this course we are dealing with data sets of *labeled examples*. Examples can be scalar numbers, rows of tabular data, images, etc. For tabular data, we refer the to columns as *explanatory variables* (sometimes also called *independent* or *descriptive* variables).\n",
        "\n",
        "Labels can be categorical, ordinal or continuous. Labels can be refered to as the *response variable* (or *dependent* variable). They are also called *targets*. Typically, we the problems are called:\n",
        "1. *Regression problems*, when the labels are continuous.\n",
        "2. *Classification problems*, when the labels are categorical.\n",
        "\n",
        "The distinction is not always clear. Some problems can be considered either as regression or classification problems.\n",
        "\n",
        "Given a ML problem, i.e. a set of labeled examples, the goal is to build a function $f$ that maps examples to labels or, in other words, that predicts the label from the example.\n",
        "\n",
        "The outputs of $f$ are called *predictions* or *predicted values*, and the actual labels of the examples are called *actual values* or *target values*.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "RP73ZCHW-5IP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Python packages"
      ],
      "metadata": {
        "id": "OV7OxFdf78XU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this ML course, the main Python packages are:\n",
        "\n",
        "\n",
        "\n",
        "1. **Pytorch**: PyTorch is an optimized tensor library for deep learning using GPUs and CPUs;  https://pytorch.org/docs/stable/index.html\n",
        "\n",
        "2. **Tensor Flow**: the alternative to PyTorch from Google.\n",
        "\n",
        "3. **Scikit-learn**: Another high-level package build on `NumPy`, `SciPy`, and `matplotlib` which covers most ML techniques except deep learning;  https://scikit-learn.org/stable/index.html.\n",
        "\n",
        "4. **Fastai**, a high-level package build from `pytorch`. A description of `fastai` is available in the paper *Howard, J.; Gugger, S. Fastai: A Layered API for Deep Learning. Information 2020, 11, 108. https://doi.org/10.3390/info11020108* and on the site https://docs.fast.ai/"
      ],
      "metadata": {
        "id": "Ly1ySlnR8AMM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Data visualization, pre-processing and feature engineering"
      ],
      "metadata": {
        "id": "-n3vZLDqdJdU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Discriminant analysis is a linear technique that helps to visualize numerical data for classification problems. Library `scikit-learn` provides the `LinearDiscriminantAnalysis` (LDA) for that purpose. LDA determines the axis along which between-class variance over within-class variance is largest.\n"
      ],
      "metadata": {
        "id": "WNpDOG7qdoSb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script to project the iris data set on the 1st discriminant axis\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "from sklearn.datasets import load_iris\n",
        "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
        "import pandas as pd\n",
        "\n",
        "# Load the Iris dataset\n",
        "iris = load_iris()\n",
        "X = iris.data\n",
        "y = iris.target\n",
        "target_names = iris.target_names\n",
        "\n",
        "# Perform Linear Discriminant Analysis\n",
        "lda = LinearDiscriminantAnalysis(n_components=1)\n",
        "X_lda = lda.fit_transform(X, y)\n",
        "\n",
        "# Combine the transformed data and target labels into a DataFrame\n",
        "data = {'LDA Component 1': X_lda.squeeze(), 'Class': target_names[y]}\n",
        "df = pd.DataFrame(data)\n",
        "\n",
        "# Plot the result\n",
        "plt.figure(figsize=(8, 6))\n",
        "sns.kdeplot(data=df, x='LDA Component 1', hue='Class', fill=True, common_norm=False)\n",
        "plt.xlabel('LDA Component 1')\n",
        "plt.title('Density of Classes over Linear Discriminant Axis')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "bNnNkHCHeOqK",
        "outputId": "02e7a861-56f4-4f39-b43f-f98220360461",
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "If there are more than 2 classes, we can define more than one discriminant axis. In particular, it is easy to visualize data projected onto the first discriminant plane as in the following example."
      ],
      "metadata": {
        "id": "D8AMizj5e-YE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script to project the iris data set on the 1st discriminant plane\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.datasets import load_iris\n",
        "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
        "\n",
        "# Load the Iris dataset\n",
        "iris = load_iris()\n",
        "X = iris.data\n",
        "y = iris.target\n",
        "\n",
        "# Perform Linear Discriminant Analysis\n",
        "lda = LinearDiscriminantAnalysis(n_components=2)\n",
        "X_lda = lda.fit_transform(X, y)\n",
        "\n",
        "# Plot the result\n",
        "plt.figure(figsize=(8, 6))\n",
        "for i, target_name in enumerate(iris.target_names):\n",
        "    plt.scatter(X_lda[y == i, 0], X_lda[y == i, 1], label=target_name)\n",
        "\n",
        "plt.xlabel('LDA Component 1')\n",
        "plt.ylabel('LDA Component 2')\n",
        "plt.title('Linear Discriminant Analysis')\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "61ooLJVbfMqU",
        "outputId": "15c80aac-f414-4bf5-a89a-e612ee900c97",
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Linear visualization techniques are not flexible enough to address problems where classes (example with the same labels) are not, at least approximately, linearly separable. There are many non-linear techniques which can be applied to large data sets that also perform dimensionality reduction and permit visualization of very complex data sets.\n",
        "\n",
        "Two relevant papers that describe fast techniques for large data sets:\n",
        "- [t-SNE-CUDA: GPU-Accelerated t-SNE and its Applications to Modern Data](https://arxiv.org/pdf/1807.11824)\n",
        "- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://arxiv.org/pdf/1802.03426)\n",
        "\n",
        "The following script illustrates those techniques, and compares them with LDA, for creating 2-dimensional and 3-dimensional plots. In the examples, three data sets are compared: `digits`, `wine` and `wine quality`."
      ],
      "metadata": {
        "id": "TlSpxtAgB6c5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script to apply dimensionality reduction techniques t-SNE, UMAP and LDA to several data sets\n",
        "!pip install umap-learn[plot]\n",
        "!pip install ucimlrepo\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.manifold import TSNE\n",
        "from umap import UMAP\n",
        "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
        "# Data\n",
        "from sklearn.datasets import load_digits, load_wine\n",
        "from ucimlrepo import fetch_ucirepo\n",
        "# plotly\n",
        "import plotly.express as px\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# constants\n",
        "DATA='wine quality' # 'digits', 'wine', 'wine quality'\n",
        "WINE_QUALITY_RESPONSE='quality' # 'color' or 'quality' for 'wine quality'\n",
        "STANDARDIZE=True\n",
        "K=3 # new data dimension\n",
        "SHOW_DIGITS=False # for 'digits'\n",
        "METHOD='umap' #'lda' #'umap' // 'tsne'\n",
        "\n",
        "# read data; returns X, y (dataframes) and labels (list with the length of y)\n",
        "if DATA=='digits':\n",
        "    digits = load_digits(as_frame=True)\n",
        "    if SHOW_DIGITS:\n",
        "        fig, ax = plt.subplots(1, 4)\n",
        "        for i in range(4):\n",
        "            ax[i].imshow(digits.images[i], cmap='Greys')\n",
        "        # plt.savefig('figures/05_12.png', dpi=300)\n",
        "        plt.show()\n",
        "    y = digits.target # dataframe\n",
        "    X = digits.data # dataframe\n",
        "    labels=['digit_'+str(i) for i in y]\n",
        "\n",
        "if DATA=='wine':\n",
        "    X, y = load_wine(return_X_y=True, as_frame=True)\n",
        "    labels=['region'+str(i) for i in y]\n",
        "\n",
        "if DATA=='wine quality':\n",
        "    # URL of the white wine dataset\n",
        "    URL = 'http://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv'\n",
        "    # load the dataset from the URL\n",
        "    white_df = pd.read_csv(URL, sep=\";\")\n",
        "    # fill the 'color' column\n",
        "    white_df[\"color\"] = 'white'\n",
        "    # keep only the first of duplicate items\n",
        "    white_df = white_df.drop_duplicates(keep='first')\n",
        "    # URL of the red wine dataset\n",
        "    URL = 'http://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv'\n",
        "    # load the dataset from the URL\n",
        "    red_df = pd.read_csv(URL, sep=\";\")\n",
        "    # fill the `color` column\n",
        "    red_df[\"color\"] = 'red'\n",
        "    # keep only the first of duplicate items\n",
        "    red_df = red_df.drop_duplicates(keep='first')\n",
        "    # concatenate to obtain full data set\n",
        "    df = pd.concat([red_df, white_df], ignore_index=True)\n",
        "    # define X and y (dataframe)\n",
        "    X = df.drop(columns=['quality','color'])\n",
        "    if WINE_QUALITY_RESPONSE=='quality':\n",
        "        y=df[WINE_QUALITY_RESPONSE] # pandas.core.series.Series\n",
        "        labels=['quality_'+str(i) for i in y]\n",
        "    if WINE_QUALITY_RESPONSE=='color':\n",
        "        y = pd.get_dummies(df[WINE_QUALITY_RESPONSE])['red'].replace({True: 1, False: 0}) # pandas.core.series.Series\n",
        "        labels=['color_'+str(i) for i in y]\n",
        "\n",
        "# standardize data\n",
        "if STANDARDIZE:\n",
        "    stdsc = StandardScaler().set_output(transform=\"pandas\")\n",
        "    X = stdsc.fit_transform(X)\n",
        "\n",
        "# dimensionality reduction\n",
        "if METHOD=='tsne':\n",
        "    #In t-SNE, the perplexity may be viewed as a knob that sets the number of effective nearest neighbors. Typically, between 5 and 50. Robust\n",
        "    tsne = TSNE(n_components=K)#, metric='mahalanobis')\n",
        "    X_ = tsne.fit_transform(X) # dataframe with K columns\n",
        "if METHOD=='umap':\n",
        "    umap=UMAP(n_components=K,n_neighbors=3,min_dist=0.1)\n",
        "    print(y,type(y))\n",
        "    X_= umap.fit_transform(X,y) # or just umap.fit_transform(X)\n",
        "if METHOD=='lda':\n",
        "    K=min(len(np.unique(labels))-1,K); print('K',K)\n",
        "    lda = LinearDiscriminantAnalysis(n_components=K)\n",
        "    X_ = lda.fit_transform(X, y)\n",
        "\n",
        "# prepare dataframe for plot with plotly.express\n",
        "proj_names=['proj'+str(i) for i in range(X_.shape[1])]\n",
        "df=pd.DataFrame(X_,columns=proj_names) # projections of X\n",
        "df['label']=labels # label\n",
        "\n",
        "# plots 2D or 3D\n",
        "def plot_projection_2D(df):\n",
        "    fig = px.scatter(df, x=proj_names[0], y=proj_names[1],color='label', title='dimension reduction with '+METHOD)\n",
        "    fig.show()\n",
        "\n",
        "def plot_projection_3D(df):\n",
        "    fig = px.scatter_3d(df, x=proj_names[0], y=proj_names[1], z=proj_names[2],color='label', title='dimension reduction with '+METHOD)\n",
        "    fig.show()\n",
        "\n",
        "if K==2:\n",
        "    plot_projection_2D(df)\n",
        "if K==3:\n",
        "    plot_projection_3D(df)"
      ],
      "metadata": {
        "id": "_w03BfRt5oEO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "f4fb4ed9-b774-4929-ab4e-7caaa85b1fbe"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: umap-learn[plot] in /usr/local/lib/python3.10/dist-packages (0.5.6)\n",
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            "0       5\n",
            "1       5\n",
            "2       5\n",
            "3       6\n",
            "4       5\n",
            "       ..\n",
            "5315    6\n",
            "5316    5\n",
            "5317    6\n",
            "5318    7\n",
            "5319    6\n",
            "Name: quality, Length: 5320, dtype: int64 <class 'pandas.core.series.Series'>\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
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    {
      "cell_type": "markdown",
      "source": [
        "# Models and parameters"
      ],
      "metadata": {
        "id": "RW_X7OPCXc3C"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "More formally, if $E$ is the set of examples and $L$ is a set that includes the labels, then what we call the *model* is a family of functions $f_{\\rm \\bf w}$ that depends on a set of parameters ${\\rm \\bf w}$: $$f_{\\rm \\bf w}: E → L.$$\n",
        "\n",
        "It can be more convenient to express the function as depending on the parameters ${\\rm \\bf w}$ as well as the example ${\\rm \\bf x}$. The model's predicted label $\\hat{y}$ for the example ${\\rm \\bf x}$ is:\n",
        "\n",
        "$$\\hat{y}=f_{\\rm \\bf w}({\\rm \\bf x})= f({\\rm \\bf x}; {\\rm \\bf w}).$$\n",
        "\n",
        "ML practicioners use an enormous variety of models, depending on the problem at hand and on the available computational resources to train the model. Models include convolucional neural networks (CNN) for image classification (resnet and other kind of CNNs), neural networks (NN) for classification of tabular data, linear regression models, decision and regression trees, random forest and other ensemble models, among many other models.\n",
        "\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1g7cUxaqoa1ujkRV-BjQKPWsVDFBAYWMb\" width=\"600\" >\n",
        "\n"
      ],
      "metadata": {
        "id": "IKZwTca7XfkW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Example of a simple model (simple linear regression)"
      ],
      "metadata": {
        "id": "xNbDdfhgXHQg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Suppose that our examples are scalar numbers $x_1,\\dots, x_n$ and the labels are continuous labels $y_1, \\dots, y_n$. We call $x$ the explanatory variable and $y$ the response variable.\n",
        "\n",
        "Let's consider the simple linear regression model:\n",
        "$f_{\\rm a,b}(x)= a \\, x + b$. The model parameters are ${\\rm \\bf w}=(a,b)$ and the predicted values are given by$\\\\[1em]$\n",
        "$$\\hat{y}=f(x; {\\rm a,b})=a\\, x + b.$$\n",
        "\n",
        "The target  or actual label values are the $y_1, \\dots, y_n$, and the predicted label values are the $\\hat{y}_1,\\dots,\\hat{y}_n$.\n",
        "\n"
      ],
      "metadata": {
        "id": "ak8k0ZkGXL5T"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Example of a simple model (quadratic regression)"
      ],
      "metadata": {
        "id": "KCwiAiilXOkJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In notebook [Lesson3_edited_04-how-does-a-neural-net-really-work.ipynb](Lesson3_edited_04-how-does-a-neural-net-really-work.ipynb), a similar simple example is discussed. The only difference is that the model $f_{\\rm a,b,c}$ in that example is quadratic instead of linear:\n",
        "\n",
        "$$f_{\\rm a,b,c}(x)= f(x;a,b,c)= a \\, x^2 + b \\, x + c.$$\n",
        "\n"
      ],
      "metadata": {
        "id": "B06MlDsTXWxi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Loss function for regression"
      ],
      "metadata": {
        "id": "TsCcLtocYK6M"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In ML, it is usual to call *loss* to the **dissimilarity** between actual and predicted label values for a *set* of labeled examples.\n",
        "\n",
        "Let ${\\rm \\bf x}_1, \\dots , {\\rm \\bf x}_n$ be a set of examples with labels $y_1, \\dots , y_n$. Let $f_{\\rm \\bf w}$ be our model. Therefore, the predicted labels are\n",
        "\n",
        "$$\\hat{y}_1=f_{\\rm \\bf w}({\\rm \\bf x}_1), \\dots, \\hat{y}_n=f_{\\rm \\bf w}({\\rm \\bf x}_n).$$\n",
        "\n",
        "The loss over that set of examples is some dissimilarity measure between the actual labels $y_1, \\dots , y_n$ and the predicted labels $\\hat{y}_1, \\dots , \\hat{y}_n$.\n",
        "\n"
      ],
      "metadata": {
        "id": "Bp8K-cntPVfx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Dissimilarity measures to define *loss*"
      ],
      "metadata": {
        "id": "9dLMWMHcYlvn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "To define loss, we then need to choose an appropriate dissimilarity metric between a set of actual $y_1, \\dots , y_n$ and predicted labels $\\hat{y}_1, \\dots , \\hat{y}_n$. The choice depends on the type of problem, and while MAE or RMSE are adequate for *regression* problems, other dissimilarities are used for *classification* problems.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "JaP8Ef2zYo24"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Examples of loss functions for regression problems (MAE, MSE, Huber)\n",
        "\n"
      ],
      "metadata": {
        "id": "TazkXj5DYsdC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Above, two common loss functions for regression problems were listed\n",
        "\n",
        "1. Mean absolute error (MAE), given by $\\frac{1}{n}\\sum_{i=1}^n |y_i-\\hat{y}_i|$; or\n",
        "\n",
        "2. Mean square error (MSE), given by $\\frac{1}{n}\\sum_{i=1}^n \\left(y_i-\\hat{y}_i\\right)^2$\n",
        "\n",
        "In the one hand, MAE is not differentiable everywhere, which is an undesirable property for ML. On the other hand, MSE penalizes too much large differences between actual and predicted values, which means that a single example can constraint strongly the solution.\n",
        "\n",
        "An alternative is called the Huber loss function, which is differentiable everywhere, and behaves like MSE near the origin and like MAE for large $|y_i-\\hat{y}_i|$.\n"
      ],
      "metadata": {
        "id": "WlJNpKjwWRLO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Examples: simple linear regression and quadratic regression\n"
      ],
      "metadata": {
        "id": "cM7AZbYpYeRO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "For the linear regression example, the response variable is continuous. We wish to measure the dissimilarity between the set of actual label values $y_1, \\dots , y_n$  and the set of values predicted by the model\n",
        "$f_{\\rm a,b}(x)= a \\, x + b$:\n",
        "\n",
        "$$\\hat{y}_1=a\\, x_1+ b, \\dots, \\hat{y}_n=a\\, x_n+ b.$$\n",
        "\n",
        "Since the response is continuous, it makes sense to use a function like the Mean absolute error (MAE), or the  Mean square error (MSE) for the loss."
      ],
      "metadata": {
        "id": "L2buuqntYha_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notebook [Lesson3_edited_04-how-does-a-neural-net-really-work.ipynb](Lesson3_edited_04-how-does-a-neural-net-really-work.ipynb) discusses a slightly more complex example, with one additional parameter. The only difference is that the generating function is quadratic instead of linear. In that new example, loss is given by MAE, i.e. $\\frac{1}{n}\\sum_{i=1}^n |y_i-\\hat{y}_i|$."
      ],
      "metadata": {
        "id": "FE79yyV8a1hQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def mae(preds, acts):\n",
        "  return (torch.abs(preds-acts)).mean()"
      ],
      "metadata": {
        "id": "P2hSIz50ckp8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The notebook includes code to interactively change the model weights and compute the corresponding values for the MAE loss function."
      ],
      "metadata": {
        "id": "Mz8gGbFccln_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "# ML as an optimization problem\n"
      ],
      "metadata": {
        "id": "BZmxXfDFYx3q"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "Now, we can define a ML problem as a optimization problem. Given\n",
        "\n",
        "1.  a set of examples  ${\\rm \\bf x}_1, \\dots , {\\rm \\bf x}_n$  with labels $y_1, \\dots , y_n$\n",
        "2. a model $f_{\\rm \\bf w}$\n",
        "3. a *loss* function $L$\n",
        "\n",
        "the goal is to determine the optimal set of parameters ${\\rm \\bf w}$ that minimize the loss $L$ over that set of examples."
      ],
      "metadata": {
        "id": "8GK-Y7gRLHC3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Gradient descent and learning rate"
      ],
      "metadata": {
        "id": "zIX1NzGbLTkI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Informally, a gradient measures how much the output of a function changes if you change the inputs a little bit.\n",
        "\n",
        "Given a model $f_{\\rm \\bf w}({\\rm \\bf x})= f({\\rm \\bf x}; {\\rm \\bf w})$ and a batch of examples ${\\rm \\bf x_1}, \\dots, {\\rm \\bf x_n}$, we have seen how we can define a *loss* function\n",
        "\n",
        "$$L({\\rm \\bf x_1, \\dots, x_n; w})= L_{\\rm \\bf x_1, \\dots, \\rm \\bf x_n}(\\rm \\bf w).$$\n",
        "\n",
        "We can write $L$ just a function of the weights since the ${\\rm \\bf x_i}$ are fixed for given batch of examples. Our goal is to find the set of weights ${\\rm \\bf w}$ that minimize $L({\\rm \\bf w})$. In order to do this iteratively, starting with an arbitrary set of initial weights, we would like to know how $L$ changes with a small change in the weights $\\rm \\bf w$ from the current set weights ${\\rm \\bf w}^{*}$.\n",
        "\n",
        "This  is given by the gradient of $L$ with respect to ${\\rm \\bf w}$ at ${\\rm \\bf w}^{*}$, which is a vector of partial derivatives of $L$ with length equal to $m$=number of model parameters.\n",
        "\n",
        "$$ \\nabla L({\\rm \\bf w}^{*}) = \\frac{\\partial L}{\\partial \\rm \\bf w}({\\rm \\bf w}^{*})= \\left(\\frac{\\partial L}{\\partial \\rm w_1}({\\rm \\bf w}^{*}), \\dots,  \\frac{\\partial L}{\\partial \\rm w_m}({\\rm \\bf w}^{*}) \\right).$$\n",
        "\n",
        "The computation of $\\nabla L({\\rm \\bf w}^{*})$ is usually done by **back-propagation**, which is an automatic differentiation algorithm for calculating gradients for the weights in a neural network graph structure. Back-propagation (aka *backprop*) is an automatic differentiation algorithm that applies the *chain-rule*.\n",
        "\n",
        "The vector $\\nabla L({\\rm \\bf w}^{*})$ points to the direction from ${\\rm \\bf w}^{*}$ along which $L$ grows faster, so gradient descent follows the opposite direction $ - \\nabla L({\\rm \\bf w}^{*})$.\n",
        "\n",
        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GA/x8zIVmJhPV+ARpAAAAAI82Q8bNvEpKENA7+IF02Dbkn0vL0LiGjB7UBkOrG/IvJO67XKaT+k6YMbqfC1vatKqSC6fPX6WnfeKezUzesdI48bAGcp3dM3GXnUzKop8Hjx5nK1JOGDOcbmpXnTmZypbUsD00eCNEIkdcSqp3aJUlhdZKmNHC6+rS02pssbroEcu/XL5oWnivLl3ch69mzkl2+g3mPUbQW3+aIORReb/+dLw2kbN5/OmFUS3O4wxxwPQP9qerytN+jp7B5vKS06tnDBr7ebLdbcMDQvoz5zc35y6zgy3/ZNtayMBg+qkoN4dZJAL8vemn+/esOk/cvXefPhZ392bdPi4UCki0NjFz+9cI8POuid/10zhB6vMFCOQAAAAADSi9eum+gXL2GxjsiC/1TSq9fjqryi14SLh1a7wDlKcfi79eYSBf/dTFN+410jXVctqzWa/MmzpjkKdAVXjm8Jl0G3mDA5aZ3GSiziSndqw0TjxsgXxISH/mOSPd3L+7aXdzzDNv1WucZPXrwzRrVzi4Wbv5zI2l5NBuWrWWzv7f7dt3WPFLmL1tDvWV9S+G+znJfCKefmf1TwlppZS0d1gfyz7sLM+XX55GAlvRzxv2sSXU8b2HmDz+3Ey2oJWkg+aviksvK764Lqob/e+c4tz781bYnZfZj8qg0zGL7feTHdCPCeQW11ZGPTmZvtk9ZcNXlhcgtMn/tzGF/BqHPD3X9iE0TCAU1L21gIRwvjmT20zjBia9C4V1CgEAAACgxv1ruQqK59nLYrazNqROPZOpkPUcP6JNbjBUVqhdg0fMn9jDjae/n5p8VcmWN0Ek8Rs6OsJPQOmKbtyqYgu5VpPJyWvy346VxomHroWcTVlZSScdG7OkMvs7crSRkIFMP/J6hyb17lHDz6N51+sKY6O6D12y6UI+1Wt6dGxSocqkURTcTv7vrLqjSZqJ5748R8ajVLtj2fuuj/+ys4iivJ//o4PyOEvsEbp4R8YZ8yB4Wd+srsn/TSiTV9BPAlGzUiUHn2yZvJx5Fomrm+7FM9euo8efy/py0tjlu68WqdVFV3cvHzd5TaaJcp//6bvN7IvB9FEn/7XstU6QTN7dv0tgD3+rNE6YawoFD+RyLwAAAECHU5mZmqOhhD6DhzJjBre1gps3Sk1G5e29Frdw048LxeRNZcbvzOLvFr1Zm8ej79ioCF8nv9DJ/Vz5+tJzh1Py7e2ELnCT0l9hK9V2hvgHwZzJyYsOl8aJhy6Qhz81len8e3rHVvZO4ib072NurazXW9hMe/lqNv3sLG2LkRSaZci0SfRdz9Tp7VsddLEh8/NpL+4qMQj6Lj1Vmrl/1fMR3o0fpDjqbXpoN1Xc1jg6kZ/etpfO41HPTTC/7VDi8FefY+4JVynkTEGTtFl3mBux6f7d9Hlqv59sZhazRzJ3i9uBPOd9/X/TPelOAatnDfKRyXwGzVp9Vi7utWhL2g9P2nfrvyWJxInH42ntu3PDZDLpdXq+QCCV2B6hEAAAAOARJ796+76ekgT0ejDd1dua1MXTfBweYSNHdhEaldmJ5wrti+SGcjX9DVMi5ay5Mi7heEmpdUIgmfzPf1pkM43brN9+PHz3kE9YNJeeVspw/OP3jmvsiOTVA5ilxO+xEXO1cQdP0X3fZWERA9gi7kx4gT20le8etytoNaEsPj6F/N3J5nz+r5HMpGZNG/UXemg31faNv2qp1N30mGl+cxe1Io83lhhdZM1Kytq4hFP0s/djI839u9vtJ5u5/zBzKWBYxGjmygFNm7x80ivx2inr0tOP/PL9ytdfiF7z/e6LZRVZP85rYBj/xgn4fCdnJ5OJHl+dLWqYRkt38pc4I40DAAAA2JR/+Y6SfD0NHuDLFjhC4fnD/4vdtXFz/OGb9bp/dwmdZ3nzds0jjO7B7hI8hlkc089cuVWk/cYMCBBRysxzB683Os8RoavMu3LmfJ6B4rkF9OBsJvL4g4mltgJ27+Ce7Ku6GqrfTjyEg7qN+nh1JH0HdN76qDmxBTYiufbmmqjna98Z8scX6PmyqJNfflxvALHC9V9tV5GKfi++4dhe2S0zauUaZl7tvPWzZsfWDoDeUnfvMTdZd/bvZjXombawiOn8bYN5aDfDgS2/Zu4/lEXOzOz5o9i3mk+bvGJw18fX3rQZygv3xF+mnwMHMh9PU1JXvrednjnMb+4LE9iY29JPtiDnHvuqDq085ejRW/LWXgop2/rXNWnkWTDhuec9ay6D7Pz0i5sGasLCxb17T3z21RXfbFq19NWnQj1aM1SeVOLE4/N1Wp3J6m7yunR6g0FvEAj5aB4HAAAAsKkq7WZmFWVrtrMamfE1vcpjd+3NoEc8q+5YzjwOZZrrWSjOuKekR/ExarLvmoc+4ogkcNI45mbyi+dSrfuh15n2bOPWhP2XitQmvnvwoCEPpOf+o+AhDOSU54Ifvov0IFFHEffSwDHLd1lMaa3N+X1NVNDAZbs2Lxz5t4tsTgl69z+L6ZbnrC8nTbUIh9qc+NfGLz2hN1Hukas/aHnqdCTPeevWRtK//Iq4hd0C/7A+xTIeqm/vXv7GRqbt1T79zcOSZ+/enFwzITalvrJmStfp/2M6f9tiHtrNcOCTyA0pJC0v/GOLz0xF/KtPrr5ZcvytgV2HvGh1KFfWzw77y0kDia1jly6rP+/6gaVj3t1/T8MukY/qh6gn/kUCLeU+68uPR9XM3dXcT3bIsMH0CVEd23e89oSwUv8xuPOwJ57o02Xsv+v/c9qgrK9mz12fRl8oMFMnLR/3AjM3et93v3ytNo9TOh3dR+j62aSmrkvaT8Dny6TO5Je8srKqoUxO0rhWo+XxeK4yG8P4AQAAAAD55n35dpnR8bOddQ7u5kKHMb5Tj+7+5iKuCPxCxwdL+Sb5xSZuJucJJR79R02MGuHDbc/9bbsT/u/bTXY+2J9pr3jmb+r384u7+jpyBL+ColLyCOrpL5NK2KJGqdSVmXdySWXyI2xRq5CI9mzokp3F5u66YjcfD/Lno1eWlKqZ3zD34Z8dOvHeYzUtgtrkz8dOev8cCUqk7oCISf0k2WdPXsqlKwv6RielrqqtSqLZ8qCh9LRgkTGmvQtq+hxXs3h33wK2jMW+FRh9KXNV/ZBpt8Kdz4f9YXMO+6fCHhtVJS8sN0dOQcD83y78HFUzU3fsTN4LcZQpMDol419D60w0rd33vM+Tm+l4KO09elpIZ6o47cCpW2rKa9STA27tOllk6yDIT+181mv2VubqWSsPRXvzh3mTFu+yOpTaj8n6SKrPoEAsprRag9itZ8jIYbJ7h89cYw69XnWiWZ+sxQnxGjxpfDCVfbpiztlT73WnqIyPQnp/eIWpZHVSUt8NHroq0/pUxM7kvxBnMonFYq1WK5B26hs+oZuqesv079/hk++FW7R/l22N6vUsk9Slnbxc6AHZWJ37jQmPmLbotecn9mrRve7qyiqVqpJ87BKJs9U04zVp3N3NRSSy2CYAAAAAAHcaD6fHTpxJTWvGeHZenTwaGunN4Sm4JUggJ3LziswvHCW/sCT16q27ufnkhT0PUpOun5PP/rwjaO7tj54QwExqXYtEz2fWpanYKpYKDn40vVedLsJi3/HRcXfp1sU6LkUztybTwczIFlmweNca+xaJbmxBi2nunfzimQFu1h2aSeR85ouT9zRsLVZMJHPVgARyY7391dz4eoavxWpIEF1En57sz0LpRRsHQTv1Jt3uTFEhH2WwJS2nKbu4blGY5T4wxL5hizbesDqS2jN46vK6RUO8LD5aca8GPlbC7k+WKNixqE5VweQNFcwbl/7el9mcIPSzugd9aTkzBLrVpxoTyYTfyA139380w3ICeIHXqOj91h8RrezH6Y1du3If/v9a+mujUlcWFpWSh7y8grwmD6VKTRbMhSSxs/UAAAAAANoBh4fThjywDTWirVrIq6o0GXdyjczkxvazv0W9GbTy3LybFw6lFfqETA7r6+ff+H256qLstKRDaerAkWOH9W6iLvfI3t5OS0rKUroEjhwZ0quHd8saUc3HTIVMHhli1yrufj6sx/spdB6//EGzJ+RqANmJoqxU8jE1dihsC7ls/p6K2Cd5PHXR1TNHkgp97Pqs7P9kyW9Myon4ejXVt4/uSfOcNs3qzu5GW8hDP71z4f0ePHaNDZ/hwtioAS/ukgdHn7n4nl+RonYctvzUHTGrPv3udImBEkTG6Ov3V7BPZZVGpa4yGY08HiUQCvU6egt8gUAmdXZ2aue/5AAAAADwaCkqkbu7ycTNm8y42bQ6naJc5e1lMfERF9oqkBNanV6no0dvtpNIJBKj32xHkLlySPA/Lzs2j9un5n6An4x7F9btf82Z5GW9Hltzp4FAbuM+AVsSXvSYtknR4Ak9/lqXx9cVkk2YMlexRc1H/tKV6ipNFd04z+PTQ7hJJZyNjQkAAAAA0JDyCnpcJReZhM9vq2/8RqNJqaLH3nNzbVGTpuO04aBuJF3LpBL7H49cGifpkmefmTENjMnFhbKtf/syjaIEE15/yzo8pr4bzGd3uQkzY9gf6fhupDPj6Ll7eDKLLZF67KSCojzDRzZweUOpZIZ68+/GLLUQOeuuMomnp5uLi9TL0w1pHAAAAADaJ4nESaPVGo3sSFNtgaycbIJsiF3mThu2kEMT7m55e+lvdk1xMOKdbdGjuW0P1mq19ABl8hP/mvb0P8/KBX3/fuHGJ9bDud3d8ud3fsux59rBiHe2R49mXzdD+2sh1x5/rdfEdfdNsvl7lT9bTKDWrBZy9hYAv5cOZvww2foSnTppWdi4NTf07vP3Fv48E93LAQAAAODhV6FUGwwGF5lUKHT8gO56vUGpUgsEAlcXjpvHCQRysEfZ2nGd/npWrNEyA7mLB/391IVPLAcJf0DaTyC/+3+TZ+xwC1CdPnYhn5wTvzdO3V9rOQFc87qsV4+xLvAavODPH//phSG+THF+6k//XvrJtiwtd2c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/z2TfqZnvM/Wz7N96Esk3PBFGUdoDzze+TRXvP/NWvo3yX/TOG9PETRWwlz5aVDCcPdw9TCZzfkHJrVJ3D54HAAAAAFcIJKFDx8waH9kyjpPPquykVjxeq4BkuJZxtYzqlzQxvvkIUjezsqN5RaKGxC8YOLi/D0Xfup5r4EoaVV0iuZsXOHh4l/pa0xUZuw/vu1Bao6fZ8fM2i0lbeuXM1l1ZZQ4Jp/z89t2nzhbVa832gfaU1WyoKbq2b9e+/Rc13g3l1/Ju7tl/ZOPmndy2MySNp27eSf7ltnurOzaQa9XqqOcO7ns+scWvTW3qH98l4VIx66Njb6UomnKdOOKJf/9PIkWpt3zwDZfIaz949o2rFqaT8ztHHY5d9tXf53AbnqJWW8g5fjg3onm379rUl98lp8Sc/dsTmv3+2c+eR87+w29Mjol80HMZeV8tH9jQ31yc9PKzk5kHtHTkX0+ceb/pGUJW/vnxKOZlnj99smlWs+w3XtqhZmr5YdvjjZUQ8glv/d8yBQn2n3zUaskyxawPcjPfn9d07iGP/+GhYObB2YwTrk2YVqtm12ifOGt+8zeAvPVPLA7hNjpNPO29j1b4k/d205pnjpBIbtr9/CvHLTbFrLc/XM5cDvUUVZ1Gq9PbH5M0TqK41Wo1WzCLGwAAAEAvYrhWXkXSUb+gSK6AQ+edyyijgxOShvtwJW5nri04eqpIyxPFJAxrmk8rdFCMH2WtLjpfwxVwim/e1FHCsIh4+xWF0DHLVy5abb/NjGLOMTSR2+Rus1NC2SMZdFH6mYv1fP+BCfPunbuK2XvPynsnjO8vpTQFB44VNo/Z+ZcK1FaeX0TivMXz7VU9snjKzBEhPgKBQMJ3vJzRs0aNGLrygYWnTp9rK5Pb0/j4pFFLF3k6uHXXHRvIKcWyf/w9SdKUoxmmtM37tGTXwqcfD2m5h6Ji582IIj+iF86eZzdNabuP0yQ7Bq/+61Otju0BiWv/87hD9DSlbdmntdnPnitqxJw9j5x91nnHwDtsbFLzTEtRyhHD2HAcOnOhw56kMSOYxmHa3LTgQ/amrfnkbsyvnk0SO7wL4vmzJ5K7/HNnHLv1hI4e3+JCApEyfgxzp1W7OI2+0p8d2X3oHy+eZLviuId4wfsfLiIVl2544a283Df+uEllE4x5qdUb7U4keFdVq0rLq9V1Gr3BYE/jfD4vPDSIOwIAAAAAvE6T9+P5KgslHDg4rkWvdLrkp6wy2j92ykj3Tv1VdaKpS/mOL9Oyci2B42fOmh7bPOf6j4xR8ilNYT7bUsWhc6+W6ilJzJDorkRife65QqM0cvTiqYPD/CRsDQKJX+iIGROG+1HmkhuXuFYkoqqslsRzZcLk2LCGSZFFin6Ro1OW3j9zRpy3J0KjqOS7RreVyRvT+MMPLuKKerE7N5CHRg9yCIUUlX78Z+aqz7hRQwtaq2KTX8G1K8wddTnnMnOoYOIvp9kHb/ewyEGx3KNG6T/9zFwiaOPs2THtDWffLmWAL/eoQ7XHTzJ5fMDY4TbueZopVbONvLlXLzN37ROLOzcMO/LJtYsCeBR99Z0UZVjSqo+yVE4G83SBcvmHb8/y4dFZf0pKWn/eJhjy4qd/aPVGd5197I/F0nRtUSQU2l97ZbWquLTKnsYjwkKavyE2G7M4ObcBAAAAAD2Lrru+f8+FEjMlCh/5yxaRmC77OSfX6Js4cUQnZu7uGkP1mfTTF6ubN1FT0oSoCCGlvnm9hCtgEvXlUpryCx8ZzhV0TmFVlY0yFGZ+3uxyAHv7MaeOfCrV1jSNqlT28yUfUGvO7D51+mpxlUpjbDg1gcC7reNNnGby2yuNE3duIHeGW/X62Lr46NbmfljAHmSXc5FJolTU4KHsZm/QwdnfdKkveOcwa3ITJRsWck/TwvOH2YM8Qrl829X966aFiSlT2Zkv1oxV+pJc/vZPt7qdy0Me3/DyOBL1mdXMBj2z8ZVR7kzCQqGARGsbO/6oUURYcGP8bp3GCXI8X4BADgAAAOAFdOmFXXsv3jLZRKHDF09pObC85nJ6vsEvblSS+xcRC5rY1KV80erls+eNUAq0FRk/ZFxraqMm2Td6eISEMpRebJjazZBbRhK1MjymaxcI6jSGFp9THZl0TRNXC4aOjA8UUeb60vOnT+/c/UPq1zs+25y2eVf6z/leHkDeXPNMbrNRGZnZt1caJ/pWIOeEJTETpjv3yPxE7qjeqqOz90CyUwy+m3sCJx6Y7DDOxl1CZr7xY0lt/qG3mHnk2Vz+wuTo2Ie2tZ5LvjNMmW9/fIarofzieRe70LtOIBQ4rK/P5/PtmdxpGrfPHiIUtigEAAAAgB5gLj677XButZknDx+1eHq8b4s4rsvOyFMroqeO9/xIQ5EsbPTE5DABZa68cr3FJG4DEsL9KbqksIjNwOrzN2qtPGV8gssdXp3xiZvUdC2g5W3uMO4YRmjCoiWTJ8aFBfuKpSImNlotZq26Iif90LZTVfZDeoPGTE4ek39vrzRO9K1APnQwO6m33+z/ZWZMd+qL34xiD00czi5K7VIf8B7i0tmPdmseHzYkjrkzJPyaewInXlvgyRnR5DHTn/+cmdr++KszAwXsumxz/57b9Uie/erKf+XZBJOfe26MgNIe+P0jnzqsAtFdIiGzdnrzXusEyeSR4aGDosId0jhhP1LYa3r+AAAAAPQR2tyMrUcK6yhpxJgpy34Z0zKNU1T51Ss1Nqvmxi6H3t1nmCyqyf2J3fzJfVlB4CdnBtzqdczKZU36RUX6UZbSAmZ0d00BOV1hWFSCfZ3gzvPzkZL4Z9C7PEmTKHBo8vh7F857aPm9JK4/svjueaOD5Txb3Y1ctjdxb2HP5OTBbZfGib4VyEeOHcH8ol39fmurtboccVGUPp+V7dq84J43cswIpmOzK2fvLuJxo5nrEvTBbdvdM4a7q8QRk145cOndyeTbR2cdPdpqLnkX5f39sTeu0tSgF/711luf/WGokETyF1a3XHy+u2QyCY/HM5lcer9sNpvFbOELBHJZsxnsAQAAAMCz6JrzR7/LKDNIg5PnzJw9XNkL2kboOh3zAVImd5jMnZ3azVZ747qh5FKxmhJHx3VpOje7yKAgHmUpyc9umfopuiJ916FjLfuimyvKq5rmemaIFL5hI4ZEydpYrb2npO0/Ul3j2M+VZPLf/+ZRp2nc6fG9R98K5OJlq+9jlkHLefv3qR10fBbPmMbOC57/4T92O8Y/U+ZZZ/OYNTSqX8xp+fNZkfryh/luCPXiZY/fxyy/xpy9WzNkO0Y98SjThV/73R9eyWy1xrnblN8q4h41cpZoQ0YMY8fv6JsGt5hUWYcPX3cy41tJUSH3qEnF+4+9kkVT/ivefXUUjzfqlf+uHsBjFp9fs6WWO6IZZxW4QsDnS6QSm42ZX50rapvRxPyRk0mRxgEAAAB6DF125uju8ypR/+ELF00cHthGvG2+nFjz2zimB3tDr+9J7plvyqwvvZBxupSmeH4RUS1meSfsU7tV3vw5q9RISUPiuzNcVBY3OlJC2VRn9/yYnqdi52mjjWV5x/b+fFldfzO/ojGAmwoytx08ueu7AwfOFVdpuWKztiYv43yujpyTtGl5th6398DRGmcBOz4umnvUUlvH9xJ9K5BT4sXvvcG0sqrTVk19ck+RkStmkGj30fu7m5JZ5JPrmHm+KfWmh+e8ndOUAG/tfWrcxHec9dEYNSmZSfv0vr81rdWlu/DRkqTH9upE7rjqJl78r79PFjIZctWUNXtbzG/mePZuE/viv54IIy/q6voZzd8Ghu7GzrdTWy1C3imjxo5k3hjtj7uOtMjUFan3hYdPXNfyO1SR+n9bmGntwkaO5TrJZ78yKnjs3XcPDp38f42dBsaOHsLcnd/3fUXLCwgVnz784nGaEkz+29sL2OXwxNP+9eEK8i1W71jz1O6mp2+zApfJZRIen282mW0Oo8lbMlto2kILhHw0jwMAAAD0oJtZl+vMlE1XdnH71y27o9tvB3ugO2qLZc82bNm/51ylzsb3jxsxil38twX71G51NWVGyj86fgBX6kxoYKCQospzmmpmbvvTm8ZoCgamjBvuy7ea1JdPHkllXv6u1B9yrqssfJ/wqcmDGi8GiKMSkqN8KIuu6MLpndvT7FV9uf3Ykdw6M08aM2ZEe6cBndHHAjlFhTy19dsVEQKSMD+aH+nnP3zqfYypw/19lWPXPP3Ei03BULn8w/cWBZEfafWR/zeyn39M0hz2sIHz/n3Zd8QQdilvBwt+t4pkV/taXf6hRKDCL3HN9rrZn+16NsotY7tDnvr2G+7s5w30bX32P7q/FVs87b3vX/8F+cPAvA3+igjyNhBzkiIUfoMWvbDq6fe71Vi/ePVy5m9O6UczBowiFc9JCpv49wLbpU/ePlhVlb6efIfC7M9HXuSggQ+nqSnKf9Hbr6bYFwnL3bHzKtsKbfr5yEnmnpHw2CNjyDeNPv5MZCzz9kwdHLZqN0XVblnz/AEtJRjzv589FdrwvRAveO+DRQHMRZeVjzVG8oTHHm1VwS5un2sEfL5CLiVhXK83tJXJSRo3GU08Hs9XwVzFAQAAAIA+jCeUBQxLmb54fIjTZjx2ajdylHLI8NZ5vbnICckR/dgJ2NokCEleMH3OiLB+cqH9OL5IETZ03NJ77iIBvBl51KQZK2clDgtR2Gd0I/gisX9I1OQ5M6fHOjbj97CtO/f/8z9fuHjjvqbXIoGBKC6ttD9wl7KK6uyL1zVaHbfdEXIkOT73xi1uuxs2zmdf2KC1WVYrV+TIeOWb3zErajUn7j/u0Q/P1hq5QzjlB9ZNDGr+ayGOWfphjnbXCjZFtXoO45X3mKnHGgkCU9buL7Paat6bwmTI+Ru541hOT/TcOrbfu8OhLTBnP7V/67P/4ExNs7M/t7atirinGLT2HFfQaOMCNunO/7LVO1d+8q2lg+Ut/j4I5PFz/7ojX8sdweC+3tlbz73Y1lWXb3s0pvl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src=\"https://drive.google.com/uc?export=view&id=1-KGjbUaR1l3z879V_eJu7JutnSutqbdC\" width=\"500\" >\n",
        "\n",
        "\n",
        "To simplify, let's suppose that all examples are visited before updating the set of weights.\n",
        "Then, the steps of gradient descent algorithm are the following. In ML, one *epoch* corresponds to the processing of the totally of examples in the data set. So, for instance, if the algorithm runs for 20 epochs, then the model is applied to all examples 20 times.\n",
        "\n",
        "---\n",
        "\n",
        "1. Choose an initial set of weights ${\\rm \\bf w}^{*}$\n",
        "\n",
        "2. For $i = 1, \\dots, E$, where $E$ is the number of epochs, do:\n",
        "\n",
        "   i) Cumpute $\\nabla L({\\rm \\bf w}^{*})$\n",
        "\n",
        "   ii) Update ${\\rm \\bf w}^{*}:={\\rm \\bf w}^{*} - \\eta \\, \\nabla L({\\rm \\bf w}^{*}) $, where $\\eta >0 $ is the learning rate.\n",
        "\n",
        "---\n",
        "\n",
        "The choice of the *learning rate* is critical for a good performance of the algorithm. A very small learning rate will permit a good approximation of the gradient flow by the algorithm (see next figure). But if the step is too small, many epochs will be needed to get a good solution.\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=12c4X3po4-xVGUJKzyKC56lwl4ZEmXqWa\" width=\"400\" >\n",
        "\n",
        "\n",
        "\n",
        "ML practicioners use many different techniques to determine the *learning rate*. In particular, the learning rate can be adaptive and change along epochs, which is a standard approach in ML. An adaptive learning rate is provided by the `fine_tune` method used in   [Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb](Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb):\n",
        "\n",
        "    learn = vision_learner(dls, resnet18, metrics=error_rate)\n",
        "    learn.fine_tune(3)\n",
        "\n",
        "In alternative, package `fastai` contains a method `lr_find()` that helps to find a adequate lerning rate, as discussed at 1:20' of Lesson 5 of [Practical Deep Learning for Coders 2022](https://course.fast.ai/), where it is used in the following chunk of code:\n",
        "\n",
        "    learn = tabular_learner(dls, metrics=accuracy, layers=[10,10])\n",
        "    learn.lr_find(suggest_funcs=(slide, valley))\n",
        "    learn.fit(16, lr=0.03)\n",
        "\n",
        "The value `0.03` used with `learn.fit` is derived from the visual interpretation of the output of `learn.lr_find(suggest_funcs=(slide, valley))` which is the following.\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1bAH7oLrIsuISeZMr749FkI1rkmDp-hw-\" width=\"500\" >\n"
      ],
      "metadata": {
        "id": "yl_HK7NvwxUi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's consider a very simple example, where we try to fit a model to a pairs of observation that are linearly related. Below, we discuss a `PyTroch` gradient descent script for the linear regression problem, and we compare the result with the optimal coefficients obtained by *least squares*. The code below shows how *training loss* is  computed.\n",
        "\n",
        "The most specific part of the algorithm is the gradient computation. Note that the *gradient machinery* of `PyTorch` is turned-on for each weight with `requires_grad = True` as in the following case:\n",
        "\n",
        "    coeffs=torch.tensor([-20.,-10.]).requires_grad_()\n",
        "\n",
        "Then, the derivatives can be computed for any continuous function of the weights in tensor `coeffs`. In particular, the *loss* $L$ is defined as a function (that can be arbitrarily complicated) of the weights, and the *gradient* $\\nabla L({\\rm \\bf w}^{*})$ for the current set of weights ${\\rm \\bf w}^{*}$ is computed with\n",
        "\n",
        "    loss.backward()\n",
        "\n",
        "Finally, the weights are updated with\n",
        "\n",
        "    coeffs.sub_(coeffs.grad * step_size)\n",
        "\n",
        "where method `sub_` is substraction for weight updating ${\\rm \\bf w}^{*}:={\\rm \\bf w}^{*} - \\eta \\, \\nabla L({\\rm \\bf w}^{*})$, and  the learning rate $\\eta$ is called `step_size` in the code.\n",
        "\n",
        "Try changing the learning rate to see what happens (try for instance `step_size=0.1`)."
      ],
      "metadata": {
        "id": "uYeKj5SFfKre"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script for stochastic gradient descent with Pytorch, train only data, applied to synthetic LR data\n",
        "# This example illustrates: gradient descent with PyTorch, train only, stochastic gradient descent (SGD)\n",
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "import numpy as np\n",
        "torch.manual_seed(42)\n",
        "\n",
        "step_size = 0.001  # learning rate\n",
        "iter = 20  # number epochs\n",
        "\n",
        "############################################ Creating synthetic data\n",
        "# Creating a function f(X) with a slope of -5\n",
        "X = torch.arange(-5, 5, 0.1).view(-1, 1)  # view converts to rank-2 tensor with one column\n",
        "func = -5 * X + 2\n",
        "# Adding Gaussian noise to the function f(X) and saving it in Y\n",
        "y = func + 0.4 * torch.randn(X.size())\n",
        "\n",
        "########################################## Baseline: Linear regression LS solution\n",
        "from sklearn.linear_model import LinearRegression\n",
        "reg = LinearRegression().fit(X, y)\n",
        "print('Least square LR coefficients:',reg.intercept_,reg.coef_)\n",
        "\n",
        "####################################################### Gradient Descent\n",
        "# initial weights\n",
        "coeffs = torch.tensor([-20., -10.], requires_grad=True)\n",
        "\n",
        "# defining the function for prediction (linear regression)\n",
        "def calc_preds(x):\n",
        "    return coeffs[0] + coeffs[1] * x\n",
        "\n",
        "# Computing MSE loss for one example\n",
        "def calc_loss_from_labels(y_pred, y):\n",
        "    return torch.mean((y_pred - y) ** 2) # mean applies to a single value in this case\n",
        "\n",
        "# lists to store losses for each epoch\n",
        "training_losses = []\n",
        "\n",
        "# epochs\n",
        "for i in range(iter):\n",
        "    # calculating loss as in the beginning of an epoch and storing it\n",
        "    y_pred = calc_preds(X)\n",
        "    loss = calc_loss_from_labels(y_pred, y)\n",
        "    training_losses.append(loss.item())\n",
        "\n",
        "    # Stochastic Gradient Descent (SGD): update weights after each data point\n",
        "    for j in range(X.shape[0]):\n",
        "        # randomly select a data point\n",
        "        idx = np.random.randint(X.shape[0])\n",
        "        x_point = X[idx]\n",
        "        y_point = y[idx]\n",
        "\n",
        "        # making a prediction in forward pass\n",
        "        y_pred = calc_preds(x_point)\n",
        "\n",
        "        # calculating the loss between predicted and actual values\n",
        "        loss = calc_loss_from_labels(y_pred, y_point)\n",
        "\n",
        "        # compute gradient\n",
        "        loss.backward()\n",
        "\n",
        "        # update coeffs\n",
        "        with torch.no_grad():\n",
        "            coeffs.sub_(coeffs.grad * step_size)\n",
        "            # zero gradients\n",
        "            coeffs.grad.zero_() # PyTorch accumulates the gradients on subsequent backward passes. So, the default action has been set to accumulate (i.e. sum) the gradients on every loss.backward() call.\n",
        "\n",
        "print('coeffs found by stochastic gradient descent:', coeffs.detach().numpy())\n",
        "\n",
        "# plot training loss along epochs\n",
        "plt.plot(training_losses, '-g')\n",
        "plt.xlabel('epoch')\n",
        "plt.ylabel('loss (MSE)')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "d198pwagfZRS",
        "outputId": "26b4e25f-7a8a-4510-e5a2-9f2f93449284",
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Least square LR coefficients: [2.0237875] [[-5.0023813]]\n",
            "coeffs found by stochastic gradient descent: [ 1.608836 -4.990727]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A simple linear model: the perceptron"
      ],
      "metadata": {
        "id": "vwfOe3xg66d0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The example above envolved a linear regression model. That model is closely related to a basic Machine Learning model which is known as the *perceptron* .\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1HqHfJn7ejJMGeAa5fTTQzW_myubIDsDh\" width=\"600\" >\n",
        "\n",
        "\n",
        "The *perceptron* model can be written as\n",
        "\n",
        "$$f_{\\rm \\bf w}(x_1,\\dots,x_k)= \\sigma (w_0 + w_1 \\, x_1 + \\dots + w_k \\, x_k)$$\n",
        "\n",
        "where $\\sigma(.)$ is called an activation function, which is defined by a discontinuity like the following one\n",
        "\n",
        "$$\\sigma(z) = \\left\\{\\begin{align}\n",
        "1 &, &  z \\ge 0 \\\\\n",
        "-1 &, &  z < 0 \\\\\n",
        "\\end{align} \\right.$$\n",
        "\n",
        "The term $w_0 + w_1 \\, x_1 + \\dots + w_k \\, x_k$ corresponds to the core component of multiple linear regression model:\n",
        "$$Y=w_0 + w_1 \\, x_1 + \\dots + w_k \\, x_k + \\varepsilon,$$\n",
        "where $\\varepsilon$ represents the random errors.\n",
        "\n",
        "For that model, the predicted values are $\\hat{y}=w_0 + w_1 \\, x_1 + \\dots + w_k \\, x_k$ and the absolute loss for each observation is $L=|\\hat{y}-y|$. Since the observation $y$ does not depend on the weights, the partial derivates of the loss with respect to the weights are simply\n",
        "$$\\nabla L({\\rm \\bf w}^{*})=(1, \\pm x_1, \\dots, \\pm x_k),$$\n",
        "where the sign depends on the sign of $\\hat{y}-y$ for each observation.\n",
        "\n",
        "The following code, which does not use `PyTorch` but just the basic funcionalities of Python and `numpy` does exactly that. This code uses object oriented programming and creates a class `Perceptron` with methods `step_fit`, where the update of the model parameters is performed, `net_input` and `predict` which are needed to apply *gradient descent*. However, since the code is used to illustrate graphically the iterative process, the code also includes several methods that are needed to create an animation with `FuncAnimation`. The algorithm is applied to the `iris` data set, to only two species at the time. Only the two first explanatory variables are used for illustrative purposes.\n"
      ],
      "metadata": {
        "id": "lq3RHqTo7HVl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script to create a Perceptron class and an animation and apply it to the iris data set\n",
        "from matplotlib.animation import FuncAnimation\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random\n",
        "import pandas as pd\n",
        "\n",
        "class Perceptron():\n",
        "    #initialize hyperparameters (learning rate and number of iterations)\n",
        "    def __init__(self, eta=0.1, n_iter=50, nameA='', nameB=''):\n",
        "        self.eta = eta\n",
        "        self.n_iter = n_iter\n",
        "        self.nameA = nameA\n",
        "        self.nameB = nameB\n",
        "\n",
        "    def step_fit(self, X, y):\n",
        "        #iterate over labelled dataset updating weights for each features accordingly (stochastic gradient descent)\n",
        "        for xi, label in zip(X, y):\n",
        "            update = self.eta * (label-self.predict(xi))\n",
        "            self.w_[1:] += update * xi\n",
        "            self.w_[0] += update\n",
        "        return self\n",
        "\n",
        "    #compute the net input i.e scalar sum of X and the weights plus the bias value\n",
        "    def net_input(self, X):\n",
        "        return np.dot(X, self.w_[1:]) + self.w_[0]\n",
        "\n",
        "    #predict a classification for a sample of features X\n",
        "    def predict(self, X):\n",
        "        return np.where(self.net_input(X) >= 0.0, 1, -1)\n",
        "\n",
        "    def init_plot(self):\n",
        "        self.line.set_data([],[])\n",
        "        return self.line,\n",
        "\n",
        "    def animate(self, iteration_number, X, y):\n",
        "        self.step_fit(X, y)\n",
        "        x, y = self.plot_line(X)\n",
        "        self.line.set_data(x, y)\n",
        "        if iteration_number%2==0:\n",
        "            self.ax.text(max(X[:,0])-0.5, min(X[:,1])+0.5, f'Iteration: {iteration_number}', fontsize=12)  # Update iteration number\n",
        "        else:\n",
        "            self.ax.text(max(X[:,0])-0.5, min(X[:,1])+0.5, 'Iteration:'+' '*8, fontsize=12, bbox=dict(facecolor='white', alpha=1))\n",
        "        return self.line,\n",
        "\n",
        "    def plot_line(self, X):\n",
        "        x = []\n",
        "        y = []\n",
        "        slope = -(self.w_[0]/self.w_[2])/(self.w_[0]/self.w_[1])\n",
        "        intercept = -self.w_[0]/self.w_[2]\n",
        "        for i in np.linspace(np.amin(X[:,0])-0.5,np.amax(X[:,0])+0.5):\n",
        "            #y=mx+c, m is slope and c is intercept\n",
        "            x.append(i)\n",
        "            y.append((slope*i) + intercept)\n",
        "\n",
        "        return x, y\n",
        "\n",
        "    def animated_fit(self, X, y):\n",
        "        self.w_ = [random.uniform(-1.0, 1.0) for _ in range(1+X.shape[1])] #randomly initialize weights\n",
        "\n",
        "        #here figure must be defined as a variable so it can be passed to FuncAnimation\n",
        "        self.fig = plt.figure()\n",
        "\n",
        "        #setting x and y limits with a 0.5 offset\n",
        "        self.ax = plt.axes(xlim=(min(X[:,0])-0.5, max(X[:,0])+0.5), ylim=(min(X[:,1])-0.5, max(X[:,1])+0.5))\n",
        "\n",
        "        #plotting our training points\n",
        "        self.ax.plot(X[0:50, 0],X[0:50, 1], \"bo\", label=self.nameA)\n",
        "        self.ax.plot(X[50:100, 0],X[50:100, 1], \"rx\", label=self.nameB)\n",
        "\n",
        "        #labelling\n",
        "        self.ax.legend(loc='upper left')\n",
        "\n",
        "        #initialization of separation line and our animation object\n",
        "        self.line, = self.ax.plot([], [], lw=2)\n",
        "        anim = FuncAnimation(self.fig, self.animate, init_func=self.init_plot, fargs=(X, y,), frames=self.n_iter, interval=200, blit=True)\n",
        "        anim.save('learning_process.gif', writer='imagemagick')\n",
        "\n",
        "#import dataset\n",
        "df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data', header=None)\n",
        "\n",
        "SPECIES_1= {'name':\"Iris-setosa\",'s':0,'end':50} #0:50 # small size\n",
        "SPECIES_2= {'name':\"Iris-versicolor\",'s':50,'end':100} # 50:100\n",
        "SPECIES_3= {'name':\"Iris-virginica\",'s':100,'end':150} # 100:150\n",
        "spA,spB=SPECIES_2,SPECIES_3\n",
        "\n",
        "#preparing our data to be understood by our model\n",
        "X = df.iloc[np.r_[spA['s']:spA['end'],spB['s']:spB['end']], [0,2]].values\n",
        "y = df.iloc[np.r_[spA['s']:spA['end'],spB['s']:spB['end']], 4].values\n",
        "#y = np.where(y == 'Iris-setosa', -1, 1)\n",
        "y = np.where(y == spB['name'], -1, 1)\n",
        "\n",
        "ppn = Perceptron(eta=0.1, n_iter=150, nameA=spA['name'], nameB=spB['name']) #initializing a new perceptron\n",
        "ppn.animated_fit(X, y)"
      ],
      "metadata": {
        "id": "7FUh-VRkLFCQ",
        "outputId": "d82f0da6-6393-44dd-dcc6-9bdaa95b1fe7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:matplotlib.animation:MovieWriter imagemagick unavailable; using Pillow instead.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mini-Batch Gradient Descent"
      ],
      "metadata": {
        "id": "9x3Bky0iU_wh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The example before is a case of *stochastic gradient descent* (SGD), where weights are updated after each single example.\n",
        "\n",
        "However, SGD can be quite erratic since all individual observation affect the search. If one observation has a large *loss*, then the weights will change abruptely to accomodate that, and this and that behaviour can jeopardize the convergence of gradient descent.\n",
        "\n",
        "In the above example using the `iris` data set, one tried to separate one species from another using SGD (relying just on two explanatory variables for the sake of visualization). As one can see in the animation, the behavior can be pretty erratic, even this is a simple problem that can be solved easily with discriminant analysis techniques.\n",
        "\n",
        "Given those limitations of SGD, the most common approach in ML is to group examples in batches and update the weights after each batch. One possibility is to include all example in one single batch which leads to the *batch gradient descent* method. In alternative, the examples can be grouped in *mini-batches* of tens or hundreds examples typically.\n",
        "\n",
        "In short, there are three main possibilities:\n",
        "1. *stochastic gradient descent*, where weights are updated after each single example;\n",
        "2. *batch gradient descent*, where weights are updated once per epoch;\n",
        "3. *mini-batch gradient descent*, which is somewhere in between the other two.\n",
        "\n",
        "The example below is an adaptation of the earlier  *linear regression* example. It illustrates how weights update are done after each mini-batch of data (i.e. this is a case of *Mini-Batch Gradient Descent*). The *loss* for all examples in a mini-batch are simply combined by the `mean` function."
      ],
      "metadata": {
        "id": "1fG2E4DuYzu8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script to learn from LR synthetic data, using mini batches, and train only\n",
        "# This LR example illustrates gradient descent with PyTorch, train only and mini-batches\n",
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "import numpy as np\n",
        "torch.manual_seed(42)\n",
        "\n",
        "B = 10  # batch size\n",
        "step_size = 0.01  # learning rate\n",
        "iter = 20  # number epochs\n",
        "\n",
        "############################################ Creating synthetic data\n",
        "# Creating a function f(X) with a slope of -5\n",
        "X = torch.arange(-5, 5, 0.1).view(-1, 1)  # view converts to rank-2 tensor with one column\n",
        "func = -5 * X + 2\n",
        "# Adding Gaussian noise to the function f(X) and saving it in Y\n",
        "y = func + 0.4 * torch.randn(X.size())\n",
        "\n",
        "# shuffle data\n",
        "indices = torch.randperm(X.size(0))\n",
        "X = X[indices]\n",
        "y = y[indices]\n",
        "\n",
        "####################################################### Gradient Descent\n",
        "# initial weights\n",
        "coeffs = torch.tensor([-20., -10.]).requires_grad_()\n",
        "\n",
        "# defining the function for prediction (linear regression)\n",
        "def calc_preds(x):\n",
        "    return coeffs[0] + coeffs[1] * x\n",
        "\n",
        "# Computing MSE loss for one batch of examples\n",
        "def calc_loss_from_labels(y_pred, y):\n",
        "    return torch.mean((y_pred - y) ** 2)\n",
        "\n",
        "# lists to store losses for each epoch\n",
        "training_losses = []\n",
        "\n",
        "# epochs\n",
        "for i in range(iter):\n",
        "    # mini-batch gradient descent: weights are updated after each batch\n",
        "    for idx_start in np.arange(0, X.shape[0], B):\n",
        "        # create batch\n",
        "        batch_X = X[idx_start:(idx_start + B), :]\n",
        "        batch_y = y[idx_start:(idx_start + B):]\n",
        "        # making a prediction in forward pass\n",
        "        y_pred = calc_preds(batch_X)\n",
        "        # calculating the loss between predicted and actual values\n",
        "        loss = calc_loss_from_labels(y_pred, batch_y)\n",
        "        # compute gradient\n",
        "        loss.backward()\n",
        "        with torch.no_grad():\n",
        "            # update coeffs\n",
        "            coeffs.sub_(coeffs.grad * step_size)\n",
        "            # zero gradients (because they add up)\n",
        "            coeffs.grad.zero_()\n",
        "\n",
        "    # calculate loss on training data for this epoch\n",
        "    y_pred_train = calc_preds(X)\n",
        "    train_loss = calc_loss_from_labels(y_pred_train, y).item() # item returns the value of the tensor as a standard Python number.\n",
        "    training_losses.append(train_loss)\n",
        "\n",
        "print('batch size:', B)\n",
        "print('coeffs found by gradient descent:', coeffs.detach().numpy()) #coeffs.requires_grad_(False))\n",
        "# plot training losses along epochs\n",
        "plt.plot(training_losses, '-g')\n",
        "plt.xlabel('epoch')\n",
        "plt.ylabel('loss (MSE)')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "CrSxR_vtvp1J",
        "outputId": "a9069fdf-a39a-436c-e995-e44313ff561d",
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "batch size: 10\n",
            "coeffs found by gradient descent: [ 1.6460457 -5.0119123]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's look again that the `iris` data set and the animation of the search process, but now considering mini-batches in alternative to the stochastic strategy. If one tries to discriminate two species which are linearly separable, the perceptron is guaranteed to converge. However, a careful choice of the values of hyperparameters *batch size* and *learning rate* is needed when the classes are not linearly separable."
      ],
      "metadata": {
        "id": "nu2bsBJULfqr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script to create a Perceptron class and an animation for the iris data set, using mini batches\n",
        "from matplotlib.animation import FuncAnimation\n",
        "from functools import partial\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random\n",
        "import pandas as pd\n",
        "\n",
        "class Perceptron():\n",
        "    #initialize hyperparameters (learning rate and number of iterations)\n",
        "    def __init__(self, eta=0.1, n_iter=50, batch_size=10, nameA='', nameB=''):\n",
        "        self.eta = eta\n",
        "        self.n_iter = n_iter\n",
        "        self.batch_size = batch_size\n",
        "        self.nameA = nameA\n",
        "        self.nameB = nameB\n",
        "\n",
        "    def step_fit(self, X, y):\n",
        "        for i in range(0, X.shape[0], self.batch_size):\n",
        "            X_batch = X[i:i+self.batch_size]\n",
        "            y_batch = y[i:i+self.batch_size]\n",
        "            errors, Loss = self.loss(X_batch,y_batch)\n",
        "            self.Loss = Loss\n",
        "            #print(self.Loss)\n",
        "            #print(errors)\n",
        "            self.w_[1:] += self.eta * X_batch.T.dot(errors)\n",
        "            self.w_[0] += self.eta * errors.sum()\n",
        "        return self\n",
        "\n",
        "    def net_input(self, X):\n",
        "        return np.dot(X, self.w_[1:]) + self.w_[0]\n",
        "\n",
        "    def predict(self, X):\n",
        "        return np.where(self.net_input(X) >= 0.0, 1, -1)\n",
        "\n",
        "    def loss(self, X, y):\n",
        "        errors = y - self.predict(X)\n",
        "        Loss = ((errors ** 2).sum()) ** 0.5\n",
        "        return errors,Loss\n",
        "\n",
        "    def shuffle(self, X, y):\n",
        "        r = np.random.permutation(len(y))\n",
        "        return X[r], y[r]\n",
        "\n",
        "    def init_plot(self):\n",
        "        self.line.set_data([],[])\n",
        "        return self.line\n",
        "\n",
        "    def animate(self, iteration_number, X, y):\n",
        "        # Shuffling the data\n",
        "        X, y = self.shuffle(X, y)\n",
        "        # Fit\n",
        "        self.step_fit(X, y)\n",
        "        x, y = self.plot_line(X)\n",
        "        self.line.set_data(x, y)\n",
        "        #loss = self.loss(X, y)\n",
        "        if iteration_number%2==0:\n",
        "            self.ax.text(min(X[:,0])+2, min(X[:,1])+0.5, f'Iteration: {iteration_number}, Loss: {round(self.Loss,4)}', fontsize=12)  # Update iteration number\n",
        "        else:\n",
        "            self.ax.text(min(X[:,0])+2, min(X[:,1])+0.5, 'Iteration:'+' '*30, fontsize=12, bbox=dict(facecolor='white', alpha=1))\n",
        "        return self.line,\n",
        "        #self.ax.text(min(X[:,0])+2, min(X[:,1])+0.5, f'Iteration: {iteration_number}, Loss: {self.Loss}', fontsize=12)\n",
        "\n",
        "    def plot_line(self, X):\n",
        "        x = []\n",
        "        y = []\n",
        "        slope = -(self.w_[0]/self.w_[2])/(self.w_[0]/self.w_[1])\n",
        "        intercept = -self.w_[0]/self.w_[2]\n",
        "        for i in np.linspace(np.amin(X[:,0])-0.5,np.amax(X[:,0])+0.5):\n",
        "            #y=mx+c, m is slope and c is intercept\n",
        "            x.append(i)\n",
        "            y.append((slope*i) + intercept)\n",
        "        return x, y\n",
        "\n",
        "    def animated_fit(self, X, y):\n",
        "        self.Loss= 0\n",
        "        self.w_ = [random.uniform(-1.0, 1.0) for _ in range(1+X.shape[1])] #randomly initialize weights\n",
        "\n",
        "        #here figure must be defined as a variable so it can be passed to FuncAnimation\n",
        "        self.fig = plt.figure()\n",
        "\n",
        "        #setting x and y limits with a 0.5 offset\n",
        "        self.ax = plt.axes(xlim=(min(X[:,0])-0.5, max(X[:,0])+0.5), ylim=(min(X[:,1])-0.5, max(X[:,1])+0.5))\n",
        "\n",
        "        #plotting our training points\n",
        "        self.ax.plot(X[0:50, 0],X[0:50, 1], \"bo\", label=self.nameA)\n",
        "        self.ax.plot(X[50:100, 0],X[50:100, 1], \"rx\", label=self.nameB)\n",
        "\n",
        "        #labelling\n",
        "        self.ax.legend(loc='upper left')\n",
        "\n",
        "        #initialization of separation line and our animation object\n",
        "        self.line, = self.ax.plot([], [], lw=2)\n",
        "        #anim = FuncAnimation(self.fig, self.animate, init_func=self.init_plot, fargs=(X, y,), frames=self.n_iter, interval=200, blit=True)\n",
        "        anim = FuncAnimation(self.fig, partial(self.animate,X=X,y=y) , init_func=self.init_plot, frames=self.n_iter, interval=200) #, blit=True) #partial(self.animate,X=X,y=y)\n",
        "        anim.save('learning_process.gif') #, writer='imagemagick')\n",
        "\n",
        "#import dataset\n",
        "df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data', header=None)\n",
        "\n",
        "SPECIES_1= {'name':\"Iris-setosa\",'s':0,'end':50} #0:50 # small size\n",
        "SPECIES_2= {'name':\"Iris-versicolor\",'s':50,'end':100} # 50:100\n",
        "SPECIES_3= {'name':\"Iris-virginica\",'s':100,'end':150} # 100:150\n",
        "spA,spB=SPECIES_2,SPECIES_3\n",
        "\n",
        "#preparing our data to be understood by our model\n",
        "X = df.iloc[np.r_[spA['s']:spA['end'],spB['s']:spB['end']], [0,2]].values\n",
        "y = df.iloc[np.r_[spA['s']:spA['end'],spB['s']:spB['end']], 4].values\n",
        "y = np.where(y == spB['name'], -1, 1) # discrete response\n",
        "\n",
        "# Creating an instance of a Perceptron object\n",
        "ppn = Perceptron(eta=0.0001, n_iter=100, batch_size=25, nameA=spA['name'], nameB=spB['name'])\n",
        "ppn.animated_fit(X, y)\n"
      ],
      "metadata": {
        "id": "0G29a60qMXUt",
        "outputId": "c4b16361-76e8-465c-9722-78945843aa6d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Train and test"
      ],
      "metadata": {
        "id": "xTke3ilGLKyf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "So far, we have trained our model using all the available examples. The risk is that the model parameters overfit to the training data, and fail to generalize to new examples, which is the goal of Machine Learning.\n",
        "\n",
        "In ML, it is costumary to distinguisgh three subsets of the examples:\n",
        "  1. *training* data set;\n",
        "  2. *development* or *dev* data set; this is also either called *test* or *validation* data set.\n",
        "  3. *holdout data set*  to provide an unbiased evaluation of a final model; in the literature, this can be confusingly called *test* or *validation* data set.\n",
        "\n",
        "In fact, the literature on machine learning often reverses the meaning of *validation* and *test* sets. In `Fastai`, the development data set is refered to as `valid` as in `RandomSplitter(valid_pct=0.2, seed=42)`, but the function in `scikit-learn` to split examples is called `train_test_split`.\n",
        "\n",
        "To prevent overfitting, one straightforward approach is to split the set of examples in two sets: *train* and *test* (which is also called ). Then, :\n",
        "  - *gradient descent* is performed over the training set; but\n",
        "  - *loss* is also computed over the dev set.\n",
        "\n",
        "The example below shows an adaptation of the code for the *linear regression* example where losses are computed and reported over the dev set."
      ],
      "metadata": {
        "id": "w4SOlIzx0I-t"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script to learn from LR synthetic data, using mini batches, and train&test\n",
        "# This example illustrates: gradient descent with PyTorch, train&test,  mini-batch\n",
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "import numpy as np\n",
        "from sklearn.model_selection import train_test_split\n",
        "torch.manual_seed(42)\n",
        "\n",
        "B=10 # batch size\n",
        "step_size = 0.1 # learning rate\n",
        "iter=20 # number epochs\n",
        "\n",
        "############################################ Creating synthetic data\n",
        "# Creating a function f(X) with a slope of -5\n",
        "X = torch.arange(-5, 5, 0.1).view(-1, 1) # view converts to rank-2 tensor with one column\n",
        "func = -5 * X + 2\n",
        "# Adding Gaussian noise to the function f(X) and saving it in Y\n",
        "y = func + 0.4 * torch.randn(X.size())\n",
        "\n",
        "##################################### Create train and test sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
        "\n",
        "####################################################### Gradient Descent\n",
        "# initial weights\n",
        "coeffs=torch.tensor([-20.,-10.]).requires_grad_()\n",
        "\n",
        "# defining the function for prediction (linear regression)\n",
        "def calc_preds(x):\n",
        "  return coeffs[0] + coeffs[1] * x\n",
        "\n",
        "# Computing MSE loss for one batch of exemples\n",
        "def calc_loss_from_labels(y_pred, y):\n",
        "  return torch.mean((y_pred - y) ** 2)\n",
        "\n",
        "# lists to store losses for each epoch\n",
        "training_losses=[]; test_losses=[]\n",
        "\n",
        "# epochs\n",
        "for i in range(iter):\n",
        "  # calculating loss as in the beginning of an epoch and storing it\n",
        "    y_pred = calc_preds(X_train)\n",
        "    training_losses.append(calc_loss_from_labels(y_pred, y_train).tolist())\n",
        "    y_pred = calc_preds(X_test)\n",
        "    test_losses.append(calc_loss_from_labels(y_pred, y_test).tolist())\n",
        "    # mini-batch gradient descent: weight are updated after each batch\n",
        "    for idx_start in np.arange(0,X_train.shape[0],B):\n",
        "        # create batch\n",
        "        batch_X=X_train[idx_start:(idx_start+B),:]\n",
        "        batch_y=y_train[idx_start:(idx_start+B):]\n",
        "        # making a prediction in forward pass\n",
        "        y_pred = calc_preds(batch_X)\n",
        "        # calculating the loss between predicted and actual values\n",
        "        loss = calc_loss_from_labels(y_pred, batch_y)\n",
        "        # compute gradient\n",
        "        loss.backward()\n",
        "        with torch.no_grad():\n",
        "            # update coeffs\n",
        "            coeffs.sub_(coeffs.grad * step_size)\n",
        "            # zerofy gradients (because they add up)\n",
        "            coeffs.grad.zero_()\n",
        "\n",
        "print('batch size:', B)\n",
        "print('coeffs found by gradient descent:',coeffs.detach().numpy())\n",
        "# plot training and test losses along epochs\n",
        "plt.plot(training_losses, '-g',  test_losses, '-r')\n",
        "plt.gca().legend(('train','test'))\n",
        "plt.ylim(0, 5)\n",
        "plt.xlabel('epoch')\n",
        "plt.ylabel('loss (MSE)')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "id": "sS0Uki84xoHN",
        "outputId": "c6bf65c4-502f-4e33-c85d-3a5a5560c42a",
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "batch size: 10\n",
            "coeffs found by gradient descent: [ 2.0202172 -4.7577853]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "High level packages like `fastai` alows us to very easily specify what is the proportion of examples which is kept aside for *testing* to prevent *overfitting* the parameters.  In general, data sets with $N$ examples is partitioned into a subset with, say $0.2 \\times N$ examples for testing and $0.8 \\times N$ examples for training like in the notebook  [Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb](Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb):\n",
        "    \n",
        "    dls = DataBlock(\n",
        "        blocks=(ImageBlock, CategoryBlock),\n",
        "        get_items=get_image_files,\n",
        "        splitter=RandomSplitter(valid_pct=0.2, seed=42),\n",
        "        get_y=parent_label,\n",
        "        item_tfms=[Resize(192, method='crop')] # try crop instead of squish\n",
        "    ).dataloaders(path)\n",
        "\n",
        "where `RandomSplitter(valid_pct=0.2, seed=42)` indicates that 20% of the examples are used for testing.\n",
        "\n",
        "The *training* data set is used to search for the optimal set of weights for the model, typically by iteratively updating the weights from a initial set of weights using *gradient descent* over the loss. The *test* data set is used to compute the same loss metric over an independent set of examples.\n",
        "\n",
        "By comparing the training and test losses it is possible to assess issues in model behaviour like *high bias/underfitting*,  *high variance/overfitting*,  and *unrepresentativeness* of either training or validation set."
      ],
      "metadata": {
        "id": "hP5GBX3zLPpQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Data preprocessing and data augmentation"
      ],
      "metadata": {
        "id": "PwjwmygpsXvI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Preprocessing tabular data will be discussed in the \"Tabular data\" section below.\n",
        "\n",
        "Preprocessing images typically comes down to (1) resizing them to a particular size (2) normalizing the color channels (R,G,B) using a mean and standard deviation. These are referred to as image transformations.\n",
        "\n",
        "In addition, one typically performs what is called data augmentation during training (like random cropping and flipping) to make the model more robust and achieve higher accuracy. Data augmentation is also a great technique to increase the size of the training data.\n",
        "\n",
        "Image transformations can be achieved with *geometric image transformation*. This is the process of altering the geometric properties of an image, such as its shape, size, orientation, or position. It involves applying mathematical operations to the image pixels or coordinates to achieve the desired transformation.\n",
        "\n",
        "Code and examples for data augmentation and transformation with PyTorch can be found in the documentation https://pytorch.org/vision/main/auto_examples/.\n",
        "\n",
        "A typical code for data transformation for color image classification can be found below. It resizes the input image, possibly flips horizontally the image, and normalizes each of the image RGB channel.\n",
        "\n",
        "```\n",
        "transforms = v2.Compose([\n",
        "    v2.RandomResizedCrop(size=(224, 224), antialias=True),\n",
        "    v2.RandomHorizontalFlip(p=0.5),\n",
        "    v2.ToDtype(torch.float32, scale=True),\n",
        "    v2.Normalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225]),\n",
        "])\n",
        "out = transforms(img)\n",
        "\n",
        "plot([img, out])\n",
        "```"
      ],
      "metadata": {
        "id": "YDdNvhqHscBx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Loss functions for classification (cross-entropy)"
      ],
      "metadata": {
        "id": "Fsp3Fh9KYwCe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Classification problems have categorical labels. Therefore, the model predictions should return the most likely label for each example.\n",
        "\n",
        "While in regression the model's output is typically an unbounded response variable (for instance, it is $f(x;a,b) = a\\, x + b$ in simple linear regression), for classification problems, it is more convenient to have:\n",
        "1. one output per label;\n",
        "2. each output being a value between 0 and 1 that can be interpreted as the probability of the label.\n",
        "\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1iD519g8QbBmOGp9SiOQsIneJnWg53SMQ\" width=\"600\" >\n",
        "\n",
        "Therefore, it is usual to have a model that outputs scores $f_1({\\rm \\bf x};{\\rm \\bf w_1}), \\dots , f_k({\\rm \\bf x};{\\rm \\bf w_k})$ for each of the $k$ possible labels, and an additional model component that converts those *raw* scores into probability-like values for the labels.\n",
        "\n",
        "You saw that kind of probabilistic output when you trained and deployed an image classifier in notebook [Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb](Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb). When you did predict the label for a new example with\n",
        "\n",
        "    is_bird,_,probs = learn.predict('bird.jpg')\n",
        "    print(is_bird,probs)\n",
        "\n",
        "you got a vector of estimated probabilities like the following:\n",
        "\n",
        "    bird tensor([0.9980, 0.0020])    \n",
        "\n",
        "where the values `0.9980, 0.0020` correspond, respectively, to labels *bird* and *forest*.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "NHRyajD_N6hv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Softmax\n",
        "\n"
      ],
      "metadata": {
        "id": "iPE1rlP3fzTA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The unormalized model outputs $f_1, \\dots, f_k$ are called *scores*, *logits* or *raw* outputs. Each score $z_i=f_i({\\rm \\bf x};{\\rm \\bf w_i})$ is converted into a [0,1] value by the *softmax* function:\n",
        "\n",
        "$$p_i=\\frac{\\exp(z_i)}{\\sum_{j=1}^k \\exp(z_j)} ~~ {\\rm which~implies~that} ~~ 0<p_i \\le 1.$$\n",
        "\n",
        "After that transformation, the classification model's probabilistic output is a vector of values $(p_1,\\dots,p_k)$, with $p_i \\ge 0$ and $\\sum p_i=1$ as required for  probability distributions. The predicted label is the one with highest $p$.\n"
      ],
      "metadata": {
        "id": "9g9P9qwTf18P"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Comparing target and predicted probability distributions\n",
        "\n"
      ],
      "metadata": {
        "id": "B-r4_0PVfthi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "While for *regression* the loss is a dissimilarity between the actual labels $y_1,\\dots,y_n$ and the predicted labels $\\hat{y}_1,\\dots,\\hat{y}_n$ for the set with $n$ examples, in *classification*  with *softmax* the loss is then a dissimilarity between the actual labels $y_1,\\dots,y_n$ and the $n$ probability vectors $(p_1,\\dots,p_k)_1, \\dots, (p_1,\\dots,p_k)_n$.\n",
        "\n",
        "To compare vectors of the same dimension, one can express each target label $y_i$ as a probabilitity distribution with 0 uncertainty. Suppose that there are 3 different possible labels (as in the `iris` data set) and the actual label of the example is the first label: then, the *target distribution* would be $(1,0,0)$ which can be  compared with the model's output probability distribution $(p_1,p_2,p_3)$. This will be illustrated with an example below.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "86MG2Jplf8LX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Loss functions in fastai\n",
        "\n"
      ],
      "metadata": {
        "id": "JeIWFIf1gCoH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "A list of `fastai` loss functions is available in https://docs.fast.ai/losses.html. In general, they are simple adaptations of `pytorch` loss functions listed in https://pytorch.org/docs/stable/nn.html#loss-functions.  The most common *loss* function for classification is called *cross-entropy*.\n",
        "\n",
        "Notebook [Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb](Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb) creates the learner with:\n",
        "\n",
        "    learn = vision_learner(dls, resnet18, metrics=error_rate)\n",
        "\n",
        "`vision_learner` allows to explicitely define the loss function  with the argument `loss_func`. Since it is not explicitely defined in the code above, we can check the default which is stored in property `loss_func`:\n",
        "\n",
        "    learn.loss_func\n",
        "\n",
        "which returns `FlattenedLoss of CrossEntropyLoss()`. This `fastai` loss is described in the Pytorch documentation as the `nn.CrossEntropyLoss` class  [https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html](https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html). Hence, the loss function that is applied in the example in the notebook is  `torch.nn.CrossEntropyLoss` that computes the cross entropy loss between input logits and target.\n",
        "\n"
      ],
      "metadata": {
        "id": "iPfaq5EUgOR_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Cross-entropy and one-hot encoding\n",
        "\n"
      ],
      "metadata": {
        "id": "qq_PFJW3gGcn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "So, what is the *loss* you see in the output when you train an image classifier in notebook [Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb](Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb)?\n",
        "\n",
        "    epoch \ttrain_loss \tvalid_loss \terror_rate \ttime\n",
        "    0 \t    1.184412 \t  1.291252 \t  0.364865 \t  00:03\n",
        "\n",
        "\n",
        "Suppose that your model (`resnet18`) was trained to classify photos of birds and forests. The last layer of the model outputs *scores* $z_1=f_1(x_1,\\dots,x_n), z_2=f_2(x_1,\\dots,x_n)$, where $z_1$ is associated to *bird*, $z_2$ is associated to *forest*.\n",
        "\n",
        "By default the loss is computed with *cross-entropy* which will allow to measure the dissimilarity between the *distribution* of scores with the target value, for all the examples in a batch of examples."
      ],
      "metadata": {
        "id": "lqWLiFHzgJjn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Consider an hypothetical case with 4 examples and 3 classes (i.e. 3 possible labels, as for the `iris`data set). Suppose that the output of the `predict` method for those 4 examples area the *scores* in the following 4$\\times$3 tensor (rows are examples, columns are classes). Columns could for instance correspond to *setosa*, *versicolor* and *virginica*."
      ],
      "metadata": {
        "id": "UCfvTqd5_b4J"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "scores=torch.tensor([[4.5,2.1,0.2],\n",
        "                     [1.3,8.3,0.8],\n",
        "                     [1.2,1.5,4.2],\n",
        "                     [5.1,0.4,2.3]])"
      ],
      "metadata": {
        "id": "pYMCDHdArmrf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Looking at the tensor above, it looks like the first and fourth examples have a higher likelihood of being *setosa*, while the second example is more likely to be *versicolor* and the third one seems to be *virginica*. Let's apply *softmax* to convert the raw outputs into probability-like values."
      ],
      "metadata": {
        "id": "9N7exOe4L6Y8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        " softs = scores.softmax(dim=1)\n",
        " torch.set_printoptions(sci_mode=False)\n",
        " softs"
      ],
      "metadata": {
        "id": "_JktsXREIxvg",
        "outputId": "2c16a2c5-7b77-4177-9434-b20dc554eb10",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[    0.9056,     0.0822,     0.0123],\n",
              "        [    0.0009,     0.9985,     0.0006],\n",
              "        [    0.0446,     0.0602,     0.8953],\n",
              "        [    0.9347,     0.0085,     0.0568]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "It is clear that the softmax rule did amplify the difference in values for each example. In each row there is one value close to 1 and the remainder values are close to 0. For each example, *cross-entropy* compares the target distribution with the probability distribution returned by *softmax*.\n",
        "\n",
        "Let's suppose that in fact, the first and last examples have actually label *setosa*, the second is actually *versicolor* and the third is actually *virginica*. Then the target distribution will be 1 for the correct label and 0 for the remaining labels. This is known as  *one-hot encoding* and it's illustrated by the rows of the following tensor (each row is one example):"
      ],
      "metadata": {
        "id": "q-ok5s3pMwFf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "one_hot_target=torch.tensor([[1.,0.,0.],\n",
        "                            [0.,1.,0.],\n",
        "                            [0.,0.,1.],\n",
        "                            [1.,0.,0.]])\n",
        "standard_target=torch.tensor([0,1,2,0],dtype=torch.long)"
      ],
      "metadata": {
        "id": "5MLo9NugNaLE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Cross-entropy loss measures the dissimilarity between the probability distribution $(p_1,p_2,p_3)$ returned by *softmax* and the target distribution $(t_1,t_2,t_3)$ for the $i$-th example with the expression, and takes values between 0 (optimal value associated to minimum uncertainty) and 1 (maximum value associated to maximum uncertainty, i.e. all probabilities are equal):\n",
        "\n",
        "$$L_i=-\\left( t_1 \\, \\log(p_1) + t_2 \\, \\log(p_2) + t_3 \\, \\log(p_3) \\right) \\in [0,1].$$\n",
        "\n",
        "In the expression above, we suppose that the probabilities are non zero.\n",
        "For the whole batch of $n$ examples, the cross-entropy loss is given by the average of the $n$ individual loss values:\n",
        "\n",
        "$$L=\\frac{1}{n} \\left( L_1+L_2+ \\dots,L_n\\right).$$\n",
        "\n",
        "This can be computed with `nn.CrossEntropyLoss()` directly from the *scores* and *target* values as shown below:"
      ],
      "metadata": {
        "id": "2ziX1cVzOkaU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#! pip install torch -U\n",
        "import torch.nn as nn\n",
        "# compute loss\n",
        "loss = nn.CrossEntropyLoss()\n",
        "output = loss(scores, one_hot_target)\n",
        "print('Cross Entropy Loss: ', output)\n",
        "# or, simply\n",
        "output = loss(scores, standard_target)\n",
        "print('Cross Entropy Loss: ', output)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NIbwzbeJp7Vg",
        "outputId": "2c7d9d11-415f-4ffc-9bdf-8432849d9348"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cross Entropy Loss:  tensor(0.0697)\n",
            "Cross Entropy Loss:  tensor(0.0697)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Assessing ML performance"
      ],
      "metadata": {
        "id": "kP-e5P8tGRD4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Error rate and accuracy"
      ],
      "metadata": {
        "id": "4VcxcaTjMHJR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Notebook [Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb](Lesson1_00_is_it_a_bird_creating_a_model_from_your_own_data.ipynb) uses  `error_rate` when creating the `learner`:\n",
        "\n",
        "    learn = vision_learner(dls, resnet18, metrics=error_rate)\n",
        "    learn.fine_tune(3)\n",
        "\n",
        "where `dls` is a `DataLoaders` object with the input data, `resnet18` is a deep CNN model. The argument `metrics=error_rate` indicates that the overall performance of the algorithm is measured proportion of mismatches between the set of actual labels $y_1, \\dots , y_n$ and the set of predicted labels $\\hat{y}_1, \\dots , \\hat{y}_n$. A very similar metric is `accuracy` which is simply `1-error_rate`.\n",
        "\n",
        "When one trains a classifier in `fastai`, the output for the training epochs looks like\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1PJ36nJ-Isu-LThJTFwRj7XwVY5qWeRfJ\" width=\"300\" >\n",
        "\n",
        "One could wonder how the  `error_rate` is computed when the data set is divided into *training* and *test* sets (as mentioned earlier, the test set is also called a *development set* of examples). In `fastai`, because the training set and test set are integrated into a single class (`dataloaders`),  by default the metrics displayed during training (as in the output above) use the test set, so the `error_rate`is computed over the validation set.\n",
        "\n",
        "At this point it should be clear what `epoch`, `train_loss`, `valid_loss` and `error_rate` in the above training output are:\n",
        "1. `epoch`: number of times that the whole set of examples has been used for prediction;\n",
        "2. `train_loss`: the value of the loss function computed with the model weights for that epoch and the training examples;\n",
        "3. `valid_loss`: the value of the loss function computed with the model weights for that epoch and the validation examples;\n",
        "4. `error_rate`: proportion of mismatches between the set of actual labels $y_1, \\dots , y_n$ and the set of predicted labels $\\hat{y}_1, \\dots , \\hat{y}_n$ computed with the model weights for that epoch and the validation examples.\n",
        "\n",
        "There are many metrics other than `error_rate` for measuring the performance of *regression* and *classification* problems. For instance, `scikit-learn` provides the metrics listed in\n",
        "https://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics. The package `fastai`  includes  all metrics from `scikit-learn` and some additional ones. The documentation is available at https://docs.fast.ai/metrics.html.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "At32ItDHGVkP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Confusion matrix (error matrix)"
      ],
      "metadata": {
        "id": "RyKdSl5bQA_C"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The confusion matrix, also called error matrix, is a very useful tool to evaluate the precision of a classifier.\n",
        "\n",
        "To compute the error matrix for a classifier ${\\bf f_{\\bf w}}({\\bf x})$ trained with a given training set of examples, the steps are the following.\n",
        "\n",
        "1. Consider a test set of examples $({\\bf x}, y)$ that were not used for training;\n",
        "\n",
        "2. Predict the labels $\\hat{y}={\\bf f_{\\bf w}}({\\bf x})$ for all examples in the test set;\n",
        "\n",
        "3. Compare the predicted labels $\\hat{y}$ with the true labels $y$ and create a two-way table where the rows represent the actual labels ($y$)  and the columns represent the predicted labels $\\hat{y}$."
      ],
      "metadata": {
        "id": "XCC_Z2qSHkOO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### How to calculate and interpret a confusion matrix"
      ],
      "metadata": {
        "id": "mDGx4dmnaVRN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code illustrated how to compute a confusion matrix for a classification task with two classes, labeled 0 and 1, and plot the result with `matplotlib´.\n",
        "\n",
        "The matrix compares the true labels of the examples `y_true` with the labels predicted by the classifier `y_pred`"
      ],
      "metadata": {
        "id": "qhVmSj5JbMZF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script that computes a confusion metrics from lists of predicted and actual labels\n",
        "from sklearn.metrics import confusion_matrix\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt # to plot\n",
        "# Actual labels\n",
        "y_true = np.array([0, 1, 0, 1, 1, 0, 1, 0, 0, 1])\n",
        "# Predicted labels\n",
        "y_pred = np.array([0, 1, 1, 1, 0, 0, 1, 0, 1, 1])\n",
        "# Compute confusion matrix\n",
        "cm = confusion_matrix(y_true, y_pred)\n",
        "# Define class labels\n",
        "classes = ['Zero', 'One']\n",
        "# Plot confusion matrix\n",
        "plt.imshow(cm, interpolation='nearest', cmap=plt.cm.Blues)\n",
        "plt.title('Confusion Matrix')\n",
        "plt.colorbar()\n",
        "tick_marks = np.arange(len(classes))\n",
        "plt.xticks(tick_marks, classes, rotation=45)\n",
        "plt.yticks(tick_marks, classes)\n",
        "plt.xlabel('Predicted label')\n",
        "plt.ylabel('True label')\n",
        "# Fill in confusion matrix with values\n",
        "thresh = cm.max() / 2.\n",
        "for i, j in np.ndindex(cm.shape):\n",
        "    plt.text(j, i, format(cm[i, j], 'd'),\n",
        "             horizontalalignment='center',\n",
        "             color='white' if cm[i, j] > thresh else 'black')\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "fBgMEFnXbAtK",
        "outputId": "78faf271-a350-4976-d8bb-ec63feba9160",
        "cellView": "form"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Accuracy metrics derived from the confusion matrix"
      ],
      "metadata": {
        "id": "GS5tglwsLGog"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In general, if there are $n$ different label values, the error matrix is $n \\times n$. For simplicity, let's just consider the $2 \\times 2$ error matrix, where correct predictions are called TP or TN, and the errors FP or FN.\n",
        "\n",
        "|           | Predicted Positive | Predicted Negative |\n",
        "|-----------|--------------------|--------------------|\n",
        "| Actual Positive | TP=True Positive     | FN=False Negative    |\n",
        "| Actual Negative | FP=False Positive| TN=True Negative|\n",
        "\n",
        "The following metrics are computed from the error matrix:\n",
        "\n",
        "---\n",
        "\n",
        "1. Classification **accuracy**.\n",
        "\n",
        "$${\\rm accuracy}=\\frac{{\\rm TP}+{\\rm TN}}{{\\rm TP}+{\\rm FN}+{\\rm FP}+{\\rm TN}}.$$\n",
        "\n",
        "If the number of actual positive examples (TP+FN) is very different from the number of negative examples (FP+TN), the largest number is going to dominate the result. For instance, is 5% of some area is burned, but the classifier just labels all pixels as non-burned, the classification accuracy will be 95%.\n",
        "\n",
        "For that example, the error matrix will look something that the following one.\n",
        "\n",
        "\n",
        "|           | Predicted Burned | Predicted Non burned |\n",
        "|-----------|--------------------|--------------------|\n",
        "| Actual Burned | TP=0   | FN=50    |\n",
        "| Actual Non burned | FP=0| TN=9050|\n",
        "\n",
        "---\n",
        "\n",
        "2. **Precision**, focused on predicted positives\n",
        "\n",
        "$${\\rm precision}=\\frac{{\\rm TP}}{{\\rm TP}+{\\rm FP}}.$$\n",
        "\n",
        "This metric focusses only on the positive examples. For the burned area example above, the precision is not defined since no predictions are positive. Consider this other example, where one aims af finding greenhouses in a certain region.\n",
        "\n",
        "\n",
        "|           | Predicted Greenhouse | Predicted Other |\n",
        "|-----------|--------------------|--------------------|\n",
        "| Actual Greenhouse | TP=80   | FN=20    |\n",
        "| Actual Other  | FP=10| TN=9090|\n",
        "\n",
        "In that case, precision is $80/(80+10) \\approx 89\\%$, while overall classification accuracy is $91.7\\%$.\n",
        "\n",
        "Precision is the complement of **commission error**:\n",
        "\n",
        "$${\\rm CE}=\\frac{{\\rm FP}}{{\\rm TP}+{\\rm FP}}.$$\n",
        "\n",
        "---\n",
        "\n",
        "3. **Recall**, focused on actual positives, and also called **sensitivity** or **true positive rate (TPR)**\n",
        "\n",
        "$${\\rm recall}=\\frac{{\\rm TP}}{{\\rm TP}+{\\rm FN}}.$$\n",
        "\n",
        "The denominator here is the total number of actual positives. This is an interesting metric if we are focused on having a very low error on missing an actual positive (a typical example is missing a tumor in medecine).\n",
        "\n",
        "For the burned area example, the classifier has the worst possible outcome since it misses all actual positives, and therefore its ${\\rm recall}=0\\%$. However, a similarly arbitrary classifier that would just predict the *positive* label for all examples would have a perfect ${\\rm recall}=100\\%$. For the greenhouse example, we have ${\\rm recall}=80\\%$.\n",
        "\n",
        "Recall is the complement of **omission error**:\n",
        "\n",
        "$${\\rm OE}=\\frac{{\\rm FN}}{{\\rm TP}+{\\rm FN}}.$$\n",
        "\n",
        "For instance, one wants the *sensitivity* of a disease test to be high to ensure that sick people are detected.\n",
        "\n",
        "---\n",
        "\n",
        "4. **Specificity**, is focused on actual negatives, and is also called **true negative rate (TNR)**\n",
        "\n",
        "$${\\rm specificity}=\\frac{{\\rm TN}}{{\\rm TN}+{\\rm FP}}.$$\n",
        "\n",
        "For instance, one wants the *specificity* of a disease test to be high to prevent healthy people from being labeled as sick.\n",
        "\n",
        "---\n",
        "\n",
        "5. **F1 score**, which averages equally *precision* and *recall*\n",
        "\n",
        "$${\\rm F1~score}= 2 \\times \\frac{{\\rm precision} \\times {\\rm recall}}{{\\rm precision} + {\\rm recall}}=\\frac{{\\rm 2\\, TP}}{{\\rm 2\\, TP}+{\\rm FP}+{\\rm FN}}.$$\n",
        "\n",
        "This is also known as the **Dice coefficient**. For the burned area example ${\\rm F1~score}=0$ since in fact the F1 score is the *harmonic mean* of precision and recall. This metric still does not take into consideration true negatives (TN) and is criticized for giving the same importance to precision and recall.\n",
        "\n",
        "---\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "q1gj3czJpVg1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "`scikit-learn` offers a function that outputs a **classification report** that includes precision, recall and F1 score, for both possible labelings of the examples."
      ],
      "metadata": {
        "id": "7pdrkiXsC-Hk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script that computes a classification report from lists of predicted and actual labels\n",
        "from sklearn.metrics import classification_report\n",
        "import numpy as np\n",
        "# Actual labels\n",
        "y_true = np.array([0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0])\n",
        "# Predicted labels\n",
        "y_pred = np.array([0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0])\n",
        "# Compute confusion matrix\n",
        "report = classification_report(y_true, y_pred)\n",
        "print(report)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pAgbYUP1DYaN",
        "outputId": "d86bedaa-c3b1-4a5d-9499-59741cfd431a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.83      0.62      0.71         8\n",
            "           1       0.57      0.80      0.67         5\n",
            "\n",
            "    accuracy                           0.69        13\n",
            "   macro avg       0.70      0.71      0.69        13\n",
            "weighted avg       0.73      0.69      0.70        13\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The output above illustrates the fact that *positive* or *negative* are not interchangeable. Since true negatives are not used to compute *precision* and *recall*, accuracy measures are not invariant with respect to labeling."
      ],
      "metadata": {
        "id": "pxJJdX2EG2Kv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Create a confusion matrix with `fastai`"
      ],
      "metadata": {
        "id": "pGfVSMcfaLwP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In [Lesson2_edited_book_02_production.ipynb](Lesson2_edited_book_02_production.ipynb), to understand in detail which  mistakes the model is making,  a confusion matrix (also called an *error matrix*) was created with\n",
        "\n",
        "    interp = ClassificationInterpretation.from_learner(learn)\n",
        "\n",
        "    interp.plot_confusion_matrix()\n",
        "\n",
        "which output was:\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1zsTJ7wh6KneWG7_QuXijy5LDlJiu3K-F\" width=\"300\" >\n",
        "\n",
        "\n",
        "The comment in the notebook for this figure is the following: The rows represent all the black, grizzly, and teddy bears in our dataset, respectively. The columns represent the images which the model predicted as black, grizzly, and teddy bears, respectively. Therefore, the diagonal of the matrix shows the images which were classified correctly, and the off-diagonal cells represent those which were classified incorrectly. This is one of the many ways that fastai allows you to view the results of your model. *It is (of course!) calculated using the validation set*.\n"
      ],
      "metadata": {
        "id": "AaA2DfU8P_9n"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Cross-validation"
      ],
      "metadata": {
        "id": "790YMMytLSow"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "When assessing accuracy is used to tune the model hyper-parameters, one should not rely solely on the training set to avoid overfitting. This means that three different sets of examples must be considered:\n",
        "\n",
        "1.  *training* data set is used to search for the optimal set of weights for the model, typically by iteratively updating the weights from a initial set of weights using *gradient descent* over the loss.\n",
        "2.  *validation* data set is used to compute the same loss metric over an independent set of examples.\n",
        "3. *test* set to evaluate the performance of the classifier.\n",
        "\n",
        "However, by partitioning the available data into three sets, we drastically reduce the number of samples which can be used for learning the model, and the results can depend on a particular random choice for the pair of (train, validation) sets (see https://scikit-learn.org/stable/modules/cross_validation.html)\n",
        "\n",
        "A solution to this problem is a procedure called **cross-validation** (CV for short. A test set should still be held out for final evaluation, but the validation set is no longer needed when doing CV. In the basic approach, called $k$-fold CV, the training set is split into k smaller sets (other approaches are described below, but generally follow the same principles). The following procedure is followed for each of the k “folds”:\n",
        "\n",
        "* A model is trained using $k-1$ of the folds as training data;\n",
        "\n",
        "* The resulting model is validated on the remaining part of the data (i.e., it is used as a test set to compute a performance measure such as accuracy).\n",
        "\n",
        "The performance measure reported by $k$-fold cross-validation is then the average of the values computed in the loop. This approach can be computationally expensive, but does not waste too much data.\n",
        "\n",
        "<img src=\"https://scikit-learn.org/stable/_images/grid_search_cross_validation.png\" width=\"500\" >"
      ],
      "metadata": {
        "id": "5pBE10qZLXVq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code uses `scikit-learn` to fit a multi layer perceptron (MLP) to classify the `iris` data set.  To implement *cross-validation*, the code relies on `cross_val_score`. Note that `X` and `y` are not split in `train`and `test` in this example since `cross validation` is used to estimate accuracy."
      ],
      "metadata": {
        "id": "s7zrcLfGS0HN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from sklearn.model_selection import cross_val_score\n",
        "from sklearn import datasets\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.neural_network import MLPClassifier\n",
        "from sklearn.pipeline import make_pipeline\n",
        "\n",
        "X, y = datasets.load_iris(return_X_y=True)\n",
        "\n",
        "# uses cross-entropy as loss function\n",
        "pipe = make_pipeline(StandardScaler(),\n",
        "                     MLPClassifier(solver='sgd',hidden_layer_sizes=(10, 5, 3), max_iter=1000,learning_rate_init=0.01,momentum=0.9))\n",
        "pipe.fit(X, y)\n",
        "scores = cross_val_score(pipe, X, y, cv=5,scoring='accuracy') # by default, StratifiedKFold for y categorical\n",
        "print(scores.mean(), scores.std())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W-jS7Xs6PHFh",
        "outputId": "b4b3c9bf-9a5d-4b5d-8295-ccffbec2e6ed"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.9200000000000002 0.09797958971132714\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "To obtain *cross-validation* predicted values, one can use `cross_val_predict` as in the following example."
      ],
      "metadata": {
        "id": "fTxxvpKpVVne"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import confusion_matrix\n",
        "from sklearn.model_selection import cross_val_predict\n",
        "y_pred=cross_val_predict(pipe, X, y, cv=5)\n",
        "confusion_matrix(y,y_pred)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LjTD4JuGU8uW",
        "outputId": "f385f563-f0ac-432a-b2bd-e400be899ef7"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[50,  0,  0],\n",
              "       [ 0, 47,  3],\n",
              "       [ 0,  1, 49]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Learning and validation curves"
      ],
      "metadata": {
        "id": "Z9dzwCn9Zi7P"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since cross validation allow us to obtain estimates of accuracy for a classifier, one can use it to analyze how training and validation accuracy vary with sample size. This can be useful to understand if the reference data set is large enough (with respect to features and the number of examples) and if the model should be made simpler or more complex (e.g. varying parameters and/or regularization)."
      ],
      "metadata": {
        "id": "ZPCPLldWZtxW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_wine # 3 classes, 178 examples, 13 variables; One could also try load_digits,fetch_olivetti_faces\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.pipeline import make_pipeline\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.model_selection import learning_curve\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# load dataset\n",
        "dataset = load_wine()\n",
        "X,y=dataset.data, dataset.target\n",
        "\n",
        "pipe = make_pipeline(StandardScaler(),RandomForestClassifier())\n",
        "\n",
        "train_sizes, train_scores, test_scores =learning_curve(estimator=pipe,\n",
        "                               X=X,\n",
        "                               y=y,\n",
        "                               train_sizes=np.linspace(0.1, 1.0, 10),\n",
        "                               cv=10,\n",
        "                               n_jobs=1)\n",
        "\n",
        "train_mean = np.mean(train_scores, axis=1)\n",
        "train_std = np.std(train_scores, axis=1)\n",
        "test_mean = np.mean(test_scores, axis=1)\n",
        "test_std = np.std(test_scores, axis=1)\n",
        "\n",
        "plt.plot(train_sizes, train_mean,\n",
        "         color='blue', marker='o',\n",
        "         markersize=5, label='Training accuracy')\n",
        "\n",
        "plt.fill_between(train_sizes,\n",
        "                 train_mean + train_std,\n",
        "                 train_mean - train_std,\n",
        "                 alpha=0.15, color='blue')\n",
        "\n",
        "plt.plot(train_sizes, test_mean,\n",
        "         color='green', linestyle='--',\n",
        "         marker='s', markersize=5,\n",
        "         label='Validation accuracy')\n",
        "\n",
        "plt.fill_between(train_sizes,\n",
        "                 test_mean + test_std,\n",
        "                 test_mean - test_std,\n",
        "                 alpha=0.15, color='green')\n",
        "\n",
        "plt.grid()\n",
        "plt.title('Learning curve')\n",
        "plt.xlabel('Number of training examples')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.legend(loc='lower right')\n",
        "plt.ylim([0.5, 1.03])\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "ds0y-p0JbOwW",
        "outputId": "681d9ec2-d9a9-4485-c4d9-fee160af8029",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        }
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "While the `learning curve` shows accuracy vs the number of examples, a `validation curve` helps to understand how accuracy varies with model parameter values and choose the best parameter value. In `scikit-learn` a parameter is indicated by `modelName___parameterName` (e.g. `randomforestclassifier__max_depth`)."
      ],
      "metadata": {
        "id": "H_01T6IJelX0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_digits\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.pipeline import make_pipeline\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.model_selection import validation_curve\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# load dataset\n",
        "dataset = load_digits()\n",
        "X,y=dataset.data, dataset.target\n",
        "\n",
        "pipe = make_pipeline(StandardScaler(),RandomForestClassifier())\n",
        "\n",
        "param_range = [5, 10, 15, 20, 25, 30]\n",
        "train_scores, test_scores = validation_curve(\n",
        "                estimator=pipe,\n",
        "                X=X,\n",
        "                y=y,\n",
        "                param_name='randomforestclassifier__max_depth',\n",
        "                param_range=param_range,\n",
        "                cv=5)\n",
        "\n",
        "train_mean = np.mean(train_scores, axis=1)\n",
        "train_std = np.std(train_scores, axis=1)\n",
        "test_mean = np.mean(test_scores, axis=1)\n",
        "test_std = np.std(test_scores, axis=1)\n",
        "\n",
        "plt.plot(param_range, train_mean,\n",
        "         color='blue', marker='o',\n",
        "         markersize=5, label='Training accuracy')\n",
        "\n",
        "plt.fill_between(param_range, train_mean + train_std,\n",
        "                 train_mean - train_std, alpha=0.15,\n",
        "                 color='blue')\n",
        "\n",
        "plt.plot(param_range, test_mean,\n",
        "         color='green', linestyle='--',\n",
        "         marker='s', markersize=5,\n",
        "         label='Validation accuracy')\n",
        "\n",
        "plt.fill_between(param_range,\n",
        "                 test_mean + test_std,\n",
        "                 test_mean - test_std,\n",
        "                 alpha=0.15, color='green')\n",
        "\n",
        "plt.grid()\n",
        "plt.title('Validation curve')\n",
        "plt.legend(loc='lower right')\n",
        "plt.xlabel('Parameter max_depth')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.ylim([0.85, 1.03])\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "XL1vD7-SfBQc",
        "outputId": "efddb14e-6e64-445a-e4d1-b273b2a7a70c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        }
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Searching the best set of hyperparameters"
      ],
      "metadata": {
        "id": "N08MVuSZJNgb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Library `scikit-learn` provides `GridSearchCV` which allows to compute cross validation estimation of the performance of the model using combinations of hyperparameter values. The combination that leads to the best score is returned as the `best_params_` property."
      ],
      "metadata": {
        "id": "k1HqCn-uMHse"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_digits\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.pipeline import make_pipeline\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.model_selection import GridSearchCV\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# load dataset\n",
        "dataset = load_digits()\n",
        "X,y=dataset.data, dataset.target\n",
        "\n",
        "pipe = make_pipeline(StandardScaler(),RandomForestClassifier())\n",
        "\n",
        "max_depth_range=[5, 10, 15, 20, 25, 30]\n",
        "ccp_alpha_range=[0.0001,0.001, 0.01]\n",
        "\n",
        "param_grid = [{'randomforestclassifier__max_depth': max_depth_range,'randomforestclassifier__ccp_alpha': ccp_alpha_range}]\n",
        "\n",
        "gs = GridSearchCV(estimator=pipe,\n",
        "                  param_grid=param_grid,\n",
        "                  scoring='accuracy',\n",
        "                  refit=True,\n",
        "                  cv=5)\n",
        "gs = gs.fit(X, y)\n",
        "print(gs.best_score_)\n",
        "print(gs.best_params_)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZQOgOiGKJdEc",
        "outputId": "b7a3a66a-affc-422e-dee3-fae137b484c4"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.9427019498607242\n",
            "{'randomforestclassifier__ccp_alpha': 0.0001, 'randomforestclassifier__max_depth': 30}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "An alternative to `GridSearchCV` is `RandomizedSearchCV`. Here, we follow the standard practice of holding out a test set, using cross-validation to choose the best parametters and finally estimate accuracy with the test set."
      ],
      "metadata": {
        "id": "C4nINDm0NqaV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.datasets import load_iris\n",
        "from sklearn.model_selection import RandomizedSearchCV, train_test_split\n",
        "from sklearn.metrics import accuracy_score\n",
        "\n",
        "# Load the Iris dataset\n",
        "iris = load_iris()\n",
        "X = iris.data\n",
        "y = iris.target\n",
        "\n",
        "# Split the dataset into training and testing sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
        "# Create a Random Forest classifier\n",
        "rf_classifier = RandomForestClassifier()\n",
        "# Define the hyperparameter grid for RandomizedSearchCV\n",
        "param_grid = {\n",
        "    'n_estimators': [100, 200, 300],\n",
        "    'max_depth': [None, 5, 10, 20],\n",
        "    'min_samples_split': [2, 5, 10],\n",
        "    'min_samples_leaf': [1, 2, 4]\n",
        "}\n",
        "# Create a RandomizedSearchCV instance\n",
        "random_search = RandomizedSearchCV(estimator=rf_classifier, param_distributions=param_grid, n_iter=10, cv=5, random_state=42)\n",
        "# Perform the random search\n",
        "random_search.fit(X_train, y_train)\n",
        "# Get the best hyperparameters and model\n",
        "best_params = random_search.best_params_\n",
        "print(best_params)\n",
        "best_model = random_search.best_estimator_  # retrieve the best model\n",
        "# Make predictions on the test set using the best model\n",
        "y_pred = best_model.predict(X_test)\n",
        "# Evaluate the accuracy of the best model\n",
        "accuracy = accuracy_score(y_test, y_pred)\n",
        "print(\"Best Model Accuracy:\", accuracy)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aQuhFywfOLy2",
        "outputId": "984cb349-9adc-4eb9-cfad-d04fd38c793c"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{'n_estimators': 300, 'min_samples_split': 5, 'min_samples_leaf': 4, 'max_depth': 10}\n",
            "Best Model Accuracy: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## ROC curve and AUC"
      ],
      "metadata": {
        "id": "KY5NEkxzCyR8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In case of binary classification, we can focus on the probability of the positive class. The usual threshold for prediction is 50% but there is no *a priori* reason to choose that threshold.\n",
        "\n",
        "Therefore, we can change this threshold value of 50%. For instance, if the threshold is set as 70%, the model predicts an observation as positive only if the predicted probability is greater than 70%. Adjusting the threshold value changes some of the predicted labels and the overall performance of the classifier. Usually, a high threshold makes the prediction of the positive class less likely. This tends to increase both the false positive rate (FPR) and the true positive rate (TPR).\n",
        "\n",
        "ROC curves typically feature true positive rate (TPR) on the Y axis, and false positive rate (FPR) on the X axis. This means that the top left corner of the plot is the “ideal” point - a FPR of zero, and a TPR of one (https://scikit-learn.org/stable/auto_examples/model_selection/plot_roc_crossval.html).\n",
        "\n",
        "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/1/13/Roc_curve.svg/220px-Roc_curve.svg.png\" width=\"400\" >\n",
        "<img src=\"https://miro.medium.com/v2/resize:fit:702/format:webp/0*pF07ZmzBqbvkvqJO.png\" width=\"400\" >\n",
        "\n",
        "The **AUC** is the area under the ROC curve. Its maximum value is 1, when the classifier is optimal. The *AUC* does not depend on the classification threshold, since it integrates all thresholds."
      ],
      "metadata": {
        "id": "353X_bP0C63m"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code shows how to compute AUC directly from the estimated classification probabilities. For instance, probabilities could be the output of a NN with a *softmax* output layer."
      ],
      "metadata": {
        "id": "_QTS57TibzD2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import roc_auc_score\n",
        "# Assuming you have predicted probabilities or scores for the positive class\n",
        "y_true = [0, 1, 1, 0, 1]\n",
        "y_scores = [0.2, 0.8, 0.6, 0.3, 0.9]\n",
        "# Compute the AUC score\n",
        "auc_score = roc_auc_score(y_true, y_scores)\n",
        "print(\"AUC:\", auc_score)\n"
      ],
      "metadata": {
        "id": "2HlHD738bqhn",
        "outputId": "b081f4f8-98e6-451c-cc42-0d3adb3b6c6d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AUC: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code draws the ROC curve and estimates the AUC for a two class problem (`iris` data set restricted to the most similar classes *versicolor* and *virginica*) using a MLP classifier and 6-fold cross-validation stratified by class."
      ],
      "metadata": {
        "id": "vTbZkjxwePAQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from sklearn.datasets import load_iris\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.metrics import auc\n",
        "from sklearn.metrics import RocCurveDisplay\n",
        "from sklearn.model_selection import StratifiedKFold\n",
        "from sklearn.neural_network import MLPClassifier\n",
        "\n",
        "iris = load_iris()\n",
        "target_names = iris.target_names\n",
        "X, y = iris.data, iris.target\n",
        "X, y = X[y != 0], y[y != 0] # drop the 'setosa' class\n",
        "n_samples, n_features = X.shape\n",
        "\n",
        "cv = StratifiedKFold(n_splits=6)\n",
        "clf = MLPClassifier(solver='sgd',hidden_layer_sizes=(10, 5, 2), max_iter=300,learning_rate_init=0.01,momentum=0.9)\n",
        "\n",
        "tprs = []\n",
        "aucs = []\n",
        "mean_fpr = np.linspace(0, 1, 100) # threshold to be considered to draw the ROC curve\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(6, 6))\n",
        "for fold, (train, test) in enumerate(cv.split(X, y)):\n",
        "    clf.fit(X[train], y[train])\n",
        "    viz = RocCurveDisplay.from_estimator(\n",
        "        clf,\n",
        "        X[test],\n",
        "        y[test],\n",
        "        name=f\"ROC fold {fold}\",\n",
        "        alpha=0.3,\n",
        "        lw=1,\n",
        "        ax=ax,\n",
        "    )\n",
        "    interp_tpr = np.interp(mean_fpr, viz.fpr, viz.tpr)\n",
        "    interp_tpr[0] = 0.0\n",
        "    tprs.append(interp_tpr)\n",
        "    aucs.append(viz.roc_auc)\n",
        "ax.plot([0, 1], [0, 1], \"k--\", label=\"chance level (AUC = 0.5)\")\n",
        "\n",
        "mean_tpr = np.mean(tprs, axis=0)\n",
        "mean_tpr[-1] = 1.0\n",
        "mean_auc = auc(mean_fpr, mean_tpr)\n",
        "std_auc = np.std(aucs)\n",
        "ax.plot(\n",
        "    mean_fpr,\n",
        "    mean_tpr,\n",
        "    color=\"b\",\n",
        "    label=r\"Mean ROC (AUC = %0.2f $\\pm$ %0.2f)\" % (mean_auc, std_auc),\n",
        "    lw=2,\n",
        "    alpha=0.8,\n",
        ")\n",
        "\n",
        "std_tpr = np.std(tprs, axis=0)\n",
        "tprs_upper = np.minimum(mean_tpr + std_tpr, 1)\n",
        "tprs_lower = np.maximum(mean_tpr - std_tpr, 0)\n",
        "ax.fill_between(\n",
        "    mean_fpr,\n",
        "    tprs_lower,\n",
        "    tprs_upper,\n",
        "    color=\"grey\",\n",
        "    alpha=0.2,\n",
        "    label=r\"$\\pm$ 1 std. dev.\",\n",
        ")\n",
        "\n",
        "ax.set(\n",
        "    xlim=[-0.05, 1.05],\n",
        "    ylim=[-0.05, 1.05],\n",
        "    xlabel=\"False Positive Rate\",\n",
        "    ylabel=\"True Positive Rate\",\n",
        "    title=f\"Mean ROC curve with variability\\n(Positive label '{target_names[1]}')\",\n",
        ")\n",
        "ax.axis(\"square\")\n",
        "ax.legend(loc=\"lower right\")\n",
        "plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 691
        },
        "id": "l0T6MZYwXYZe",
        "outputId": "1b273dbd-4610-47d3-eac2-11c222239245"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:686: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (300) reached and the optimization hasn't converged yet.\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:686: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (300) reached and the optimization hasn't converged yet.\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:686: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (300) reached and the optimization hasn't converged yet.\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Some models for ML"
      ],
      "metadata": {
        "id": "emfh_GZQagkJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Tabular data"
      ],
      "metadata": {
        "id": "buB1nxDccH5M"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Simple linear regression and quadratic regression have *scalar* inputs, i.e. each example was described by a single number.\n",
        "\n",
        "Examples can also be tabular data, where each example is described by a numeric vector. Formally, the $i$-th example is described by a vector  $(x_{i1}, \\dots, x_{ik})$ of length $k$, for examples $i = 1, \\dots, n$ and labels are $y_1, \\dots,  y_n$  as before.\n",
        "\n",
        "One example of data organized in a nummerical table are the [Wine quality data set](https://www.kaggle.com/datasets/yasserh/wine-quality-dataset) available n Kaggle. It has 12 explanatory variables and the label is the wine quality.\n",
        "\n",
        "    Input variables (based on physicochemical tests):\\\n",
        "    1 - fixed acidity\n",
        "    2 - volatile acidity\n",
        "    3 - citric acid\n",
        "    4 - residual sugar\n",
        "    5 - chlorides\n",
        "    6 - free sulfur dioxide\n",
        "    7 - total sulfur dioxide\n",
        "    8 - density\n",
        "    9 - pH\n",
        "    10 - sulphates\n",
        "    11 - alcohol\n",
        "    Output variable (based on sensory data):\n",
        "    12 - quality (score between 0 and 10)\n",
        "\n",
        "But tables can also have non-numerical (text) columns like (https://www.kaggle.com/datasets/zsinghrahulk/covertype-forest-cover-types)\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "ZxwIpE1oavEr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Decision trees"
      ],
      "metadata": {
        "id": "gnji-_ie0Ta4"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "All possible examples lie on a multi-dimensional region $R$ which is the feature space. Any classifier determines a partition of $R$ into regions $R_1,\\dots,R_c$, where $R_j$ is the decision region for the $j$th class.\n",
        "\n",
        "A binary **decision tree** represents $R$ as a tree, where the *root node* represents the whole of $R$. Each node can be split into two new subnodes. The nodes that are not split are called *leaf nodes*. A class label is assigned to each *leaf node* to determine the classifier."
      ],
      "metadata": {
        "id": "uGr3ml_T7E0h"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### First example"
      ],
      "metadata": {
        "id": "cYuu8wlz7F5w"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "The example below shows a decision tree for the `iris` data set. The root node represents the 4-dimensional space defined by the variables `sepal length`,`sepal width`, `petal length`, `petal width`. This is a 3-class problem where labels are the varieties `setosa`, `versicolor`, `virginica`.\n",
        "\n",
        "We call **depth** of the decision tree to the maximum number of splits to define a leaf node. Note that the code establishes `max_depth=4` to prevent the tree from growing more than 4 levels. The figure indicates the number of examples (or training samples) that lie in each node of the tree."
      ],
      "metadata": {
        "id": "sFMtFxzXVKYa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_iris\n",
        "from sklearn import tree\n",
        "from matplotlib import pyplot as plt\n",
        "iris = load_iris()\n",
        "\n",
        "X = iris.data\n",
        "y = iris.target\n",
        "print(' labels: ', iris.target_names)\n",
        "\n",
        "#build decision tree\n",
        "clf = tree.DecisionTreeClassifier(criterion='entropy', max_depth=4,min_samples_leaf=4)\n",
        "#max_depth represents max level allowed in each tree, min_samples_leaf minumum samples storable in leaf node\n",
        "\n",
        "#fit the tree to iris dataset\n",
        "clf.fit(X,y)\n",
        "\n",
        "#plot decision tree\n",
        "fig, ax = plt.subplots(figsize=(10, 10)) #figsize value changes the size of plot\n",
        "tree.plot_tree(clf,ax=ax,feature_names=['sepal length','sepal width','petal length','petal width'])\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "J8nrDgCb0fBw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 844
        },
        "outputId": "4fe87650-63ba-4dfa-9922-cbdb8b2366fc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " labels:  ['setosa' 'versicolor' 'virginica']\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x1000 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Impurity and loss"
      ],
      "metadata": {
        "id": "tthMwNfB7MUn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "To build a tree, several questions arise:\n",
        "1. Which feature should be tested at a node?\n",
        "2. When should a node be declared a *leaf*?\n",
        "3. If the tree becomes 'too large' how can it be made smaller and simpler (pruning)?\n",
        "4. If a leaf node is impure, how should the category label be assigned?\n",
        "5. How should be missing data handled?\n",
        "\n"
      ],
      "metadata": {
        "id": "unvWp50boozw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "To answer to those questions, we first need to define a measure of the quality of the model. As before, one defines a *loss* for a decision tree since the  ultimate goal is to find the model with the lowest loss.\n",
        "\n",
        "There are two types of decision trees in ML:\n",
        "1. **Classification trees**, where the labels are categorial as in the `iris`data set example. In that case, the **predicted** label is the most frequent label in the examples that lie the leaf node. For instance, if there are $[0,3,1]$ samples of varieties `[setosa, versicolor, virginica]` in a leaf node, then the label of the leaf node is `versicolor` and this is the predicted label $\\hat{y}$ for all examples that lie in that region. To compute the *loss* one relies on the distribution of labels in the leaf node. For instance, the node with $[0,3,1]$ examples has estimated probabilities $\\hat{p}_1=0$,  $\\hat{p}_2=0.75$, $\\hat{p}_3=0.25$ of been assigned to each one of the classes.\n",
        "2. **Regression trees**, where the labels are continuous. In that case, the label for the node is the mean of all labels of examples that lie in that node, i.e. $\\hat{y}=\\bar{y}$. The *loss* for the $i$th example is then the dissimilarity between $\\bar{y}$ and $y_i$. For *regression trees* the usual *loss* functions  are `mse`and `mae`.\n"
      ],
      "metadata": {
        "id": "3AWt-NhQfkaO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's see how the *loss* of a classification tree is computed in general and of a split in particular is computed. The loss is related to the impurity of the leaf nodes of the tree. The highest is the impurity of the leaf nodes, the largest is the classification uncertainty and the loss.\n",
        "\n",
        "For any given node of the tree, with $n_1,n_2,\\dots,n_c$ examples of each class, the estimated probabilities for the $c$ different labels are:\n",
        "\n",
        "$$\\hat{p_1}=\\frac{n_1}{n},\\dots,\\hat{p_c}=\\frac{n_c}{n},$$\n",
        "\n",
        "where $n$ is the total number of examples at the node. For classification trees, the `DecisionTreeClassifier` class in `scikit-learn` uses one of the following criteria:\n",
        "\n",
        "1. `gini`: This is the default criterion and it measures the impurity of a set of samples as the probability of misclassifying a randomly chosen element from the set. The *loss* is given by  $G = 1 - \\sum_{i=1}^n p_i^2$, where $\\hat{p}_i$ is the estimated probability of belonging to the $i$th class.\n",
        "2. `entropy`: This criterion measures the impurity of a set of samples as the amount of information gained about the label from observing the features that define the node. The *loss* is given by $E=-\\sum_{i=1}^n \\hat{p}_i \\log_2 \\hat{p}_i$.\n",
        "\n",
        "Both measures range from 0 (minimum impurity, maximum certainty) to some maximum value (maximum impurity, minimum certainty). For instance, for a 2-class problem, maximum impurity is reached when $p_1=p_2=0.5$, where\n",
        "\n",
        "$$G=1-0.5=0.5 {\\rm ~and ~~} E= - 2 \\times (0.5 \\, \\log_2 0.5)= - 2 \\times (-0.5)=1.$$\n",
        "\n",
        "When the node is split into two new children nodes, the loss function is calculated separately for each subset resulting from the split, and the *total loss* is the weighted sum of the losses of the subsets, where the weights are the fractions of samples in each subset. The split with the lowest total loss (i.e., the greatest reduction in entropy) is chosen as the best split. The expression for the loss of a split is the following, where $L$ can be either the entropy $E$ or the Gini criterion $G$.\n",
        "\n",
        "$$\n",
        " L = \\frac{n_{\\rm left}}{n} \\times L_{\\rm left} + \\frac{n_{\\rm right}}{n} \\times L_{\\rm right} ~~~~~~~~~(1)$$\n",
        "\n",
        "The rules above allow us to compute the loss for any tree computed from the data set. For each new split, Equation 1 allows us to update the *loss* of the whole tree.\n",
        "\n",
        "For the two loss function above (`entropy` and `gini`), it is guaranteed that the *total loss* of the tree cannot increase for any possible split. Therefore, there is always a reduction (strict or not) in *loss*  resulting from a split which is also called *information gain*.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "LoCk_P6M0W6P"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Choosing the possible splits"
      ],
      "metadata": {
        "id": "H0vamxVJ8QpA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For continuous explanatory variables, all $n$ examples are ordered for the  $j$th feature:\n",
        "\n",
        "$$x_{j(1)} \\le x_{j(2)} \\dots \\le  x_{j(n)}.$$\n",
        "\n",
        "Hence, it is not necessary to test more than $n$ splits for each feature $j$. The spliting algorithm is just something like below.\n",
        "\n",
        "---\n",
        "Initialize $L$ as an empty list\n",
        "\n",
        "For $j=1,\\dots,k$\n",
        "\n",
        "$~~~~$ For $ i = 1, \\dots n$,\n",
        "\n",
        "$~~~~$ $~~~~$ Consider the split $x_j \\le x_{j(i)}$, compute its loss decrease and append it to $L$.\n",
        "\n",
        "The best split is the split $x_j \\le x_{j(i)}$ which has the lowest value in $L$.\n",
        "\n",
        "----"
      ],
      "metadata": {
        "id": "adazc97h8jMh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For categorical explanatory variables, when there is no order along values, in principle all $2^m$ combinations of the $m$ distinct values that the variable can take should be considered as possible splits."
      ],
      "metadata": {
        "id": "6UprQkjDCkAL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Regularization and pruning"
      ],
      "metadata": {
        "id": "-dhhbPuQFxCC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Decision trees are prone to *overfitting* since that if they grow enough they can approximate any decison rule with arbitrary precision. Therefore, there are different techniques to prevent decision trees of being  too large.\n",
        "\n",
        "1. Criterion to stop growing the tree, which is equivalent to decide when a node should not be splited and should become a leaf node. There are three standard hyper-parameters:\n",
        "  - Maximum depth of the tree (e.g. 4);\n",
        "  - Minimum leaf size, i.e., minimum number of examples that lie in a leaf (e.g. 3);\n",
        "  - Maximum number of nodes (e.g. 20).\n",
        "\n",
        "2. Pruning. This is a regularization technique that consists on pruning the full grown tree to reduce its size. Pruning can be achieved by:\n",
        "  - Adding a regularization hyper-parameter to the loss function, like $\\alpha(|T|)$ where $\\alpha$ is a function of the size (number of leaves) of the tree $T$. If one uses $L_\\alpha=L+\\alpha$ (consider that $\\alpha >0$) instead of $L$ to determine the *loss*, then spliting a node might possibly cause an increase of $L_\\alpha$.  If two leaves are pure and have the same label, aggregating them will lower $L_\\alpha$ for $\\alpha>0$. Pruning aggregates leaf nodes if that reduces $L_\\alpha$.\n",
        "  - Predicting a validation data set with the decision tree. Pruning consists of aggregating leaf nodes if that aggregation increases validation accuracy."
      ],
      "metadata": {
        "id": "XschSedhGEJ7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The script below illustrates how a regularization parameter like $\\alpha$ can be adjusted when fitting a decision tree (suggestion: try with a different data set)."
      ],
      "metadata": {
        "id": "wHvh6PajWfIT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_iris,load_wine,load_digits,fetch_olivetti_faces\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# load the iris dataset\n",
        "dataset = load_iris() #fetch_olivetti_faces() #load_digits() #load_wine() #\n",
        "\n",
        "# split the dataset into training and validation sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(dataset.data, dataset.target, test_size=0.2, random_state=42)\n",
        "\n",
        "# create a decision tree classifier\n",
        "#tree = DecisionTreeClassifier()\n",
        "\n",
        "alphas=[k/100 for k in range(10)]\n",
        "trees=[]\n",
        "# fit tree for each alpha\n",
        "for alpha in alphas:\n",
        "  # create decision tree with a cost complexity parameter alpha\n",
        "  tree = DecisionTreeClassifier(random_state=42, ccp_alpha=alpha)\n",
        "  # fit\n",
        "  tree.fit(X_train, y_train)\n",
        "  # append tree to trees\n",
        "  trees.append(tree)\n",
        "\n",
        "# compute accuracies\n",
        "train_scores = [clf.score(X_train, y_train) for clf in trees]\n",
        "test_scores = [clf.score(X_test, y_test) for clf in trees]\n",
        "\n",
        "# plot accuracy vs alpha\n",
        "fig, ax = plt.subplots()\n",
        "ax.set_xlabel(\"alpha\")\n",
        "ax.set_ylabel(\"accuracy\")\n",
        "ax.set_title(\"Accuracy vs alpha for training and testing sets\")\n",
        "ax.plot(alphas, train_scores, marker=\"o\", label=\"train\", drawstyle=\"steps-post\")\n",
        "ax.plot(alphas, test_scores, marker=\"o\", label=\"test\", drawstyle=\"steps-post\")\n",
        "ax.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "id": "-s0tNC7YUJva",
        "outputId": "23225ec0-a5ad-4c4f-a9c3-cfb4a17f72da",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Decision tree bias and variance"
      ],
      "metadata": {
        "id": "FMGFRXvy8dxh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Bias** measures how much the predictions of a model differ from the true values. **Variance** measures how much the predictions of a model differ from each other. One possible technique to estimate  bias and variance is **cross-validation**.\n",
        "\n",
        "In general, cross-validation is a technique used to evaluate the performance of a machine learning model. It involves splitting the dataset into multiple subsets, training the model on some of them, and testing it on the remaining subsets. This allows us to estimate the performance of the model on new, unseen data.\n",
        "\n",
        "The code below relies on `validation_curve`from `scikit-learn` to estimate bias and variance of a classification model. In fact, the code applies a family of models (decision trees) that depend on the hyper-parameter `max_depth`.  Note that the synthetic data set is generated by `make_classification`.\n"
      ],
      "metadata": {
        "id": "XhEYgwmM9XlH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import make_classification\n",
        "from sklearn.model_selection import validation_curve\n",
        "from sklearn import tree\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# generate a toy dataset\n",
        "X, y = make_classification(n_samples=1000, n_features=10, random_state=42,n_classes=2)\n",
        "\n",
        "# define the model\n",
        "model = tree.DecisionTreeClassifier(criterion='entropy', min_samples_leaf=4)\n",
        "\n",
        "# define the range of hyperparameters to test\n",
        "param_range = np.arange(4, 10)\n",
        "\n",
        "# use validation_curve to compute training and validation scores for different hyperparameters\n",
        "train_scores, test_scores = validation_curve(\n",
        "    model, X, y,\n",
        "    param_name=\"max_depth\", param_range=param_range,\n",
        "    cv=5,\n",
        "    scoring=\"accuracy\")\n",
        "\n",
        "# calculate the mean and standard deviation of the training and validation scores for each hyperparameter\n",
        "train_mean = np.mean(train_scores, axis=1)\n",
        "train_std = np.std(train_scores, axis=1)\n",
        "test_mean = np.mean(test_scores, axis=1)\n",
        "test_std = np.std(test_scores, axis=1)\n",
        "\n",
        "# plot the validation curves\n",
        "plt.plot(param_range, train_mean, label=\"Training score\", color=\"darkorange\")\n",
        "plt.fill_between(param_range, train_mean - train_std, train_mean + train_std, alpha=0.2, color=\"darkorange\")\n",
        "plt.plot(param_range, test_mean, label=\"Cross-validation score\", color=\"navy\")\n",
        "plt.fill_between(param_range, test_mean - test_std, test_mean + test_std, alpha=0.2, color=\"navy\")\n",
        "plt.legend(loc=\"best\")\n",
        "plt.xlabel(\"max_depth\")\n",
        "plt.ylabel(\"Accuracy\")\n",
        "plt.show()\n",
        "\n",
        "# calculate bias and variance\n",
        "bias = (1 - test_mean) ** 2\n",
        "variance = test_std ** 2\n",
        "\n",
        "print(\"Bias:\", bias)\n",
        "print(\"Variance:\", variance)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "id": "qGYQrLvP-4DD",
        "outputId": "17bee46d-fa5e-4b98-888d-cfbb11b8fe4a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Bias: [0.012996 0.010201 0.013225 0.015129 0.014884 0.013689]\n",
            "Variance: [0.000414 0.000424 0.00035  0.000346 0.000306 0.000226]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the example above, *bias* and *variance* are estimated from the validation scores. For instance, for the model with `max_depth=4`, the estimated bias is $\\approx 0.013$, which corresponds to an estimated 87% accuracy, while the estimated variance is $\\approx 0.0004$, which is the plotted standard deviation ($\\approx 0.02$) squared.\n",
        "\n",
        "Suggestion: try the code above using the `gini` instead of the `entropy` criterion for spliting."
      ],
      "metadata": {
        "id": "2fZ1mQV8HF3p"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Ensemble methods"
      ],
      "metadata": {
        "id": "-pGf7xgxbsYK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "See article about [the wisdow of the crouds](https://www.npr.org/sections/13.7/2018/03/12/592868569/no-man-is-an-island-the-wisdom-of-deliberating-crowds) for an introduction to ensemble methods."
      ],
      "metadata": {
        "id": "pdOf9i4csyd-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Random forests"
      ],
      "metadata": {
        "id": "V8DUmPknSgy5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Random forests (RF) are an ensemble learning method that involves:\n",
        "  - (bootstraping) Creating a collection of decison trees from bootstrap samples (sampling with replacement);\n",
        "  - (decorrelating) Decorrelate models by randomly selecting features\n",
        "  - (aggregating) Ensembling the collection of trees by majority vote.\n"
      ],
      "metadata": {
        "id": "9VunI0E-bOAg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<img src=\"https://miro.medium.com/v2/resize:fit:1400/format:webp/0*qSZ93ucUL8gpZ3jf.png\" width=\"800\" >"
      ],
      "metadata": {
        "id": "WrTL4F-Gd8-V"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The goal of ensemble decision trees with random forests is to reduce the variance. This is illustrated below for  regression trees. The idea for classification trees is similar but the mathematics are more complicated.\n",
        "\n",
        "Let  $X_i$ be  the random variable  that represents the predition for the regression tree $T_i$ from the collection, with $\\rho={\\rm cor}[X_i,X_j]$ being the correlation between $X_i$ and $X_j$. The prediction from the ensemble is\n",
        "\n",
        "$$ \\bar{X} = \\frac{1}{B} \\left( X_1+\\dots+X_B \\right)$$\n",
        "\n",
        "and its variance is given by\n",
        "\n",
        "$${\\rm Var}[\\bar{X}]=  \\rho \\, \\sigma^2 + \\frac{1-\\rho}{B} \\sigma^2,$$\n",
        "\n",
        "where ${\\rm Var}[X_i]=\\sigma^2$ and $B$ is the number of bootstrap samples. As long as $\\rho$ does not grow with $B$, using a larger ensemble will increase $B$ and reduce ${\\rm Var}[\\bar{X}]$, which is the goal of ensembling classifiers.\n",
        "\n",
        "Therefore, the idea of **bootstrap aggregation**, aka **bagging** is to create an ensemble of low correlated tree models (bootstrap) followed by aggregation in order to reduce the variance of the predictions."
      ],
      "metadata": {
        "id": "NP3YEtmIgRcB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Example of script that creates and fits a RF classifier for a classification problem on the `iris` data set."
      ],
      "metadata": {
        "id": "kTkN1mcDI7Ys"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.datasets import load_wine\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import accuracy_score\n",
        "import pandas as pd\n",
        "\n",
        "# load the iris dataset\n",
        "dataset = load_wine() #\n",
        "\n",
        "# Split the dataset into training and testing sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(dataset.data, dataset.target, test_size=0.2)\n",
        "# Create a Random Forest classifier\n",
        "rf_classifier = RandomForestClassifier(n_estimators=100, random_state=42)\n",
        "# Train the classifier\n",
        "rf_classifier.fit(X_train, y_train)\n",
        "# Make predictions on the test set\n",
        "y_pred = rf_classifier.predict(X_test)\n",
        "# Evaluate the accuracy of the classifier\n",
        "accuracy = accuracy_score(y_test, y_pred)\n",
        "print(\"Accuracy:\", accuracy)\n"
      ],
      "metadata": {
        "id": "bNIb0o3VIWmz",
        "outputId": "c21b9d35-dc9f-4fca-f5c6-abd6b4943b7f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 0.9444444444444444\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### AdaBoost"
      ],
      "metadata": {
        "id": "J5ljon7TTmnc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Gradient boosting is one of the variants of ensemble methods where you create multiple **weak** models  and combine them to get better performance as a whole. The original idea behind AdaBoost is described in the paper *Schapire, R.E. The strength of weak learnability. Mach Learn 5, 197–227 (1990). https://doi.org/10.1007/BF00116037*.\n",
        "\n",
        "A weak model, also called weak inducer, is a classifier that performs just better than random. For decision trees (the most common model), the weakest model is a decision tree with depth 1 which is called a **stump**.\n",
        "\n",
        "As discussed in [(Sagi and Rokach, 2017)](docs/Sagi_2018_Ensemble_learning_A_survey_Wire.pdf), the\n",
        "main idea of AdaBoost (adaptive boosting) is to focus on instances that were previously misclassified when training a new inducer. The\n",
        "level of focus given is determined by a **weight** that is assigned to each instance in the training set. In the first iteration,\n",
        "the same weight is assigned to all of the instances. In each iteration, the weights of misclassified instances are increased,\n",
        "while the weights of correctly classified instances are decreased. In addition, weights are also assigned to the individual\n",
        "base learners based on their overall predictive performance.\n",
        "\n",
        "**AdaBoost** is a *dependent* ML method since each tree is an improvement over previous trees in the sequence. This is the opposite of *random forests* where the tree are grown independently."
      ],
      "metadata": {
        "id": "apY-QFYL_89t"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<img src=\"https://www.researchgate.net/profile/Zhuo-Wang-36/publication/288699540/figure/fig9/AS:668373486686246@1536364065786/Illustration-of-AdaBoost-algorithm-for-creating-a-strong-classifier-based-on-multiple_W640.jpg\" width=\"800\" >"
      ],
      "metadata": {
        "id": "TDbAVv6qVlpQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Gradient Boosting"
      ],
      "metadata": {
        "id": "Aad1s7GgTsiz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Gradient Boost is also a *dependent* method, since each weak classifier  (they are often decision trees) is an improvement of the earlier model.  Gradient boosting trees usually have from 8 to 32 terminal nodes, i.e. depth between 3 and 5.\n",
        "\n",
        "Gradient Boosting provides a framework to build an ensemble of trees based on an arbitrary loss function and a **learning rate**. In Gradient Boosting, each new tree is computed over the **residuals** from the previous model.\n",
        "\n",
        "<img src=\"https://miro.medium.com/v2/resize:fit:720/format:webp/1*uDdVWe5-MJyy27an4Yp8GQ.png\" width=\"800\" >\n",
        "\n",
        "\n",
        "For details and very nice illustrations, look at the two following posts:\n",
        "\n",
        "1. [Regression](https://towardsdatascience.com/all-you-need-to-know-about-gradient-boosting-algorithm-part-1-regression-2520a34a502)\n",
        "\n",
        "2. [Classification](https://towardsdatascience.com/all-you-need-to-know-about-gradient-boosting-algorithm-part-2-classification-d3ed8f56541e)"
      ],
      "metadata": {
        "id": "5aZ4jZQWWCYp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Variable importance"
      ],
      "metadata": {
        "id": "IBsGmc7NT1L9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "See [(Scornet, 2021)](https://arxiv.org/pdf/2001.04295.pdf) for an in-depth presentation of the topic."
      ],
      "metadata": {
        "id": "4zkB84sjzyxq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since interpretability is a concept difficult to define precisely, people eager to gain\n",
        "insights about the driving forces at work behind random forests predictions often focus\n",
        "on variable importance, a measure of the influence of each input variable to predict\n",
        "the output. In Breiman’s [2001] original random forests, there exist two importance\n",
        "measures:\n",
        "\n",
        "1. **Mean Decrease Impurity** [MDI, or Gini importance, see Breiman, 2002],\n",
        "which sums up the gain associated to all splits performed along a given variable; and\n",
        "\n",
        "2. **Mean Decrease Accuracy** [MDA, or **permutation importance**, see Breiman, 2001]\n",
        "which shuffles entries of a specific variable in the test data set and computes the\n",
        "difference between the error on the permuted test set and the original test set.\n",
        "\n",
        "Because\n",
        "of its very definition, MDI is an importance measure that can be computed for trees\n",
        "only, since it strongly relies on the tree structure, whereas MDA is an instantiation of\n",
        "the permutation importance that can be used for any predictive model. Both measures\n",
        "are used in practice even if they possess several major drawbacks:\n",
        "  - **MDI** is known to favor variables with many categories [see, e.g., Strobl et al.,\n",
        "2007, Nicodemus, 2011]. Even when variables have the same number of categories,\n",
        "MDI exhibits empirical bias towards variables that possess a category having a high frequency [Nicodemus, 2011, Boulesteix et al., 2011]. MDI is also biased in presence of correlated features [Nicodemus and Malley, 2009].\n",
        "\n",
        "  - **MDA** seems to exhibit less bias than MDI but tends to overestimate correlated features Strobl et al. [2008]. See Genuer et al. [2008] and Genuer et al. [2010] for an extensive simulation study about the influence of the number of observations, variables, and trees on MDA together with the impact of correlation on this importance measure.\n"
      ],
      "metadata": {
        "id": "iQYeKgtBzaiZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code show how to compute MDI with different ensemble methods, and compares the estimated importances for the `iris`data set explanatory variables."
      ],
      "metadata": {
        "id": "aJVlj09w0N1r"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.datasets import load_iris\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.ensemble import AdaBoostClassifier\n",
        "from sklearn.ensemble import GradientBoostingClassifier\n",
        "\n",
        "# Load the Iris dataset\n",
        "iris = load_iris()\n",
        "X = iris.data\n",
        "y = iris.target\n",
        "feature_names = iris.feature_names\n",
        "\n",
        "# Create Random Forest classifier\n",
        "rf_clf = RandomForestClassifier(random_state=42)\n",
        "rf_clf.fit(X, y)\n",
        "\n",
        "# Create AdaBoost classifier with decision tree base estimator\n",
        "ada_clf = AdaBoostClassifier(estimator=DecisionTreeClassifier(max_depth=3), random_state=42)\n",
        "ada_clf.fit(X, y)\n",
        "\n",
        "# Create Gradient Boosting classifier\n",
        "gb_clf = GradientBoostingClassifier(random_state=42)\n",
        "gb_clf.fit(X, y)\n",
        "\n",
        "# Extract feature importance (MDI) for each classifier\n",
        "rf_importance = rf_clf.feature_importances_\n",
        "ada_importance = ada_clf.feature_importances_\n",
        "gb_importance = gb_clf.feature_importances_\n",
        "\n",
        "# Set up the figure\n",
        "fig, ax = plt.subplots(figsize=(8, 6))\n",
        "\n",
        "# Plot the feature importance\n",
        "x = np.arange(len(feature_names))\n",
        "width = 0.2\n",
        "\n",
        "rects1 = ax.bar(x - width, rf_importance, width, label='Random Forest')\n",
        "rects2 = ax.bar(x, ada_importance, width, label='AdaBoost')\n",
        "rects3 = ax.bar(x + width, gb_importance, width, label='Gradient Boosting')\n",
        "\n",
        "# Add labels, title, and legend\n",
        "ax.set_xlabel('Features')\n",
        "ax.set_ylabel('Importance')\n",
        "ax.set_title('Feature Importance Comparison')\n",
        "ax.set_xticks(x)\n",
        "ax.set_xticklabels(feature_names)\n",
        "ax.legend()\n",
        "\n",
        "# Show the plot\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "xZppyT8nT7T_",
        "outputId": "38ff3581-5418-4632-e18d-1b3a62aa5bbb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "`scikit-learn` also provides functions to compute MDA (permutation importance). This measure of importance can be computed for any classification method but it is more computationally demanding since data have to be classified after each variable is shuffled, while MDI just uses the losses (or gains) that are computed while training the classifier."
      ],
      "metadata": {
        "id": "RA3dGmYz0wgD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_iris\n",
        "from sklearn.inspection import permutation_importance\n",
        "from sklearn.neural_network import MLPClassifier\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "iris = load_iris()\n",
        "target_names = iris.target_names\n",
        "X, y = iris.data, iris.target\n",
        "feature_names = iris.feature_names\n",
        "\n",
        "# models\n",
        "rf_clf = RandomForestClassifier(random_state=42)\n",
        "rf_clf.fit(X, y)\n",
        "mlp_clf = MLPClassifier(solver='sgd',hidden_layer_sizes=(10, 5, 2), max_iter=300,learning_rate_init=0.01,momentum=0.9)\n",
        "mlp_clf.fit(X, y)\n",
        "\n",
        "# Compute permutation importance\n",
        "result_rf = permutation_importance(rf_clf, X, y,n_repeats=10)\n",
        "result_mlp = permutation_importance(mlp_clf, X, y,n_repeats=10)\n",
        "\n",
        "# Sort the importances in descending order\n",
        "sorted_importances_idx = result_rf.importances_mean.argsort()[::-1]\n",
        "\n",
        "# Plotting\n",
        "fig, ax = plt.subplots(figsize=(8, 6))\n",
        "ax.barh(np.arange(len(feature_names)), result_rf.importances_mean[sorted_importances_idx], xerr=result_rf.importances_std[sorted_importances_idx], height=0.6, color='skyblue', label='Random Forest')\n",
        "ax.barh(np.arange(len(feature_names)), result_mlp.importances_mean[sorted_importances_idx], xerr=result_mlp.importances_std[sorted_importances_idx], height=0.4, color='lightgreen', label='MLP')\n",
        "\n",
        "ax.set_yticks(np.arange(len(feature_names)))\n",
        "ax.set_yticklabels(np.array(feature_names)[sorted_importances_idx])\n",
        "ax.set_xlabel('Importance')\n",
        "ax.set_title('Feature Importance Comparison')\n",
        "ax.legend()\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 662
        },
        "id": "RpqJJgAm4PHO",
        "outputId": "d9d05b3d-c18b-4c91-f6b6-742882cf7518"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/sklearn/neural_network/_multilayer_perceptron.py:686: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (300) reached and the optimization hasn't converged yet.\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Perceptron"
      ],
      "metadata": {
        "id": "NdYeA9JQ_GT0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The *perceptron* is one of the simplest models for numerical tabular data and 0/1 classification problems and has been already discussed earlier. Since it is the basis for neural networks, we review below its formalism.\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1HqHfJn7ejJMGeAa5fTTQzW_myubIDsDh\" width=\"600\" >\n",
        "\n",
        "\n",
        "The model is\n",
        "\n",
        "$$f_{\\rm \\bf w}(x_1,\\dots,x_k)= \\sigma (w_1 \\, x_1 + \\dots + w_k \\, x_k)$$\n",
        "\n",
        "where $\\sigma(.)$ is the activation function, and it is defined by\n",
        "\n",
        "$$\\sigma(z) = \\left\\{\\begin{align}\n",
        "1 &, &  z \\ge t \\\\\n",
        "0 &, &  z < t \\\\\n",
        "\\end{align} \\right.$$\n",
        "\n",
        "where $t$ is some *threshold*.\n"
      ],
      "metadata": {
        "id": "9k6m_gN4aqDZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here, we consider that the input data as already been pre-processed, and all explanatory variables $(x_{i1},\\dots,x_{ik})$ are numerical, while the response variable is $y_i \\in \\{0,1\\}$ for $n$ examples $i=1,\\dots,n$. In practice, pre-processing is usually necessary to create the numerical inputs of the neural network.\n",
        "\n",
        "In matrix form, each row represents one example. For $n$ examples $i=1,\\dots,n$, the following matrices represent the examples and the labels.\n",
        "\n",
        "$\n",
        "\t{\\rm \\bf X}= \\begin{bmatrix}\n",
        "\tx_{11} & \\dots & x_{1k} \\\\\n",
        "\tx_{21} & \\dots & x_{2k} \\\\\n",
        "\t\\dots & \\dots & \\dots\\\\\n",
        "\tx_{n1} & \\dots & x_{nk} \\\\\n",
        "\t\\end{bmatrix}~~~~~~\n",
        "$\n",
        "$\n",
        "\t{\\rm \\bf y}= \\begin{bmatrix}\n",
        "\ty_1  \\\\\n",
        "\ty_2  \\\\\n",
        "\t\\dots \\\\\n",
        "\ty_n  \\\\\n",
        "\t\\end{bmatrix}\n",
        "$\n",
        "\n",
        "Since each example corresponds to a row of ${\\rm \\bf X}$, the $i$-th example is  $(x_{i1},\\dots,x_{ik})$\n",
        "and has label $y_i \\in \\{0,1\\}$.\n",
        "\n",
        "Although in the original medel of the Perceptron, the activation function was a step functon (see above), it is currently more common to use a continuous functions for $\\sigma(.)$. A typical  candidate is the *sigmoid* function\n",
        "\n",
        "$$\\sigma(z)= \\frac{1}{1+e^{-z}}$$\n",
        "\n",
        "that ranges between 0 and 1. This function is available in `pytorch` through `torch.sigmoid`. Another is the ReLu function in the next section which is still continuous but not differentiable.\n",
        "\n"
      ],
      "metadata": {
        "id": "pfmqoyLshvns"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import sympy\n",
        "sympy.plot(\"1/(1+exp(-z))\", xlim=(-5,5));\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "LvOfeyF8X72_",
        "outputId": "99c9e99a-94d4-40ea-9af0-773abb0f12a9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Feed-forward fully connected neural network with ReLu units"
      ],
      "metadata": {
        "id": "O0Bsy-6bLa-V"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The next step is to add more layers to the model. Instead of having just one output from the first (input) layer, the model can have many units in the following *hidden* layers. In general, the number of model outputs (output layer) is equal to the number of labels (one is enough for the Titanic problem, since the prediction is just \"survived\" or not). As mentioned earlier, typically there is either a *sigmoid* unit or a *softmax* layer to complete the model, so the final outputs can be interpreted as probabilities.\n",
        "\n",
        "This model is also known as the *Multilayer Perceptron* (MLP).\n",
        "\n",
        "If all the intermediate layers would just multiply inputs by weights, the model could be reduced to a single matrix multiplication layer. Therefore, there must some non-linearity after each matrix multiplication. That's what is described in the following figure, where $f$ represents some non-linear *activation function* for each layer of the neural network.\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1Ky82nfC7GUp7YBqp1Spzn9aHDrTzbiCH\" width=\"600\" >\n",
        "\n",
        "The layer is called *fully connected* when each matrix multiplication, which returns the dot product $x_1 \\, w_1 + \\dots + x_n \\, w_n$ envolves all neurons from the previous layer.\n",
        "\n",
        "Typically, all activation functions ($f$ in the figure above) for the *hidden layers* are called rectified linear units (*ReLu*) and they represent the following continuous function, which is the identity function for positive arguments and *zero* for negative arguments.\n",
        "\n",
        "${\\rm ReLu}(z) = \\left\\{\\begin{align}\n",
        "z &, &  z \\ge 0 \\\\\n",
        "0 &, &  z < 0 \\\\\n",
        "\\end{align} \\right.$\n",
        "\n",
        "If there is only one output, the activation layer for the *output layer* is typically the *sigmoid* function. If there is more than one output (as in the figure above), the typical choice of activation function for the output layer is the *softmax* function.\n",
        "\n",
        "For first *neuron* in the first hidden unit, the calculation goes exactely as  we discussed for the perceptron model, where the inputs are multiplied by the  weights $w_1^{(1)},\\dots, w_4^{(1)}$ to return\n",
        "\n",
        "$$w_1^{(1)} \\, x_1 + w_2^{(1)} \\, x_2 + w_3^{(1)} \\, x_3 + w_4^{(1)} \\, x_4 .$$\n",
        "\n",
        "The same product is computed for the second neuron of the first hidden layer, but for a *different set of weights* $w_1^{(2)},\\dots, w_4^{(2)}$, and so on. Hence, in total there are for the example in the figure above, 12 multiplicative weights (4 input variables $\\times$ 3 neuros in the hidden layer). The three multiplications (for the three neurons in the hidden layer) can all be done with a single matrix multiplication:\n",
        "\n",
        "If the weights and input values are  $~~~~~\n",
        "\t{\\rm W}= \\begin{bmatrix}\n",
        "\tw_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)} & w_{4}^{(1)} \\\\\n",
        "\tw_{1}^{(2)} & w_{2}^{(2)} & w_{3}^{(2)} & w_{4}^{(2)} \\\\\n",
        "\tw_{1}^{(3)} & w_{2}^{(3)} & w_{3}^{(3)} & w_{4}^{(3)} \\\\\n",
        "\t\\end{bmatrix}~~~{\\rm and}~~~~\n",
        "$\n",
        "$\n",
        "\t{\\rm x}= \\begin{bmatrix}\n",
        "\tx_1  \\\\\n",
        "\tx_2 \\\\\n",
        "\tx_3  \\\\\n",
        "\tx_4  \\\\\n",
        "\t\\end{bmatrix}~~~\n",
        "$\n",
        "\n",
        "then, the hidden layer three outputs (before applying the activation function) are just the rows of the product ${\\rm W} \\, {\\rm x}$:\n",
        "\n",
        "$$ {\\rm  W} \\, {\\rm x}= \\begin{bmatrix}\n",
        "\tw_1^{(1)} \\, x_1 + w_2^{(1)} \\, x_2 + w_3^{(1)} \\, x_3 + w_4^{(1)} \\, x_4  \\\\\n",
        "\tw_1^{(2)} \\, x_1 + w_2^{(2)} \\, x_2 + w_3^{(2)} \\, x_3 + w_4^{(2)} \\, x_4  \\\\\n",
        "\tw_1^{(3)} \\, x_1 + w_2^{(3)} \\, x_2 + w_3^{(3)} \\, x_3 + w_4^{(3)} \\, x_4  \\\\\n",
        "\t\\end{bmatrix}\n",
        ".$$\n",
        "\n",
        "This is very convenient since matrix multiplication can be computed quickly.\n",
        "\n",
        "Note that it is usual to include also an *additive weight* for each neuron (this is called the *bias*). Without lost of generality, we can think that $x_1$ is an artificial input which value is always 1, and therefore $w_1^{(j)} \\times x_1=w_1^{(j)}$ is the additive weight. In alternative, we can add a weight $w_0^{(j)}$ to each neuron, so the neuron output (before applying the activation function) is\n",
        "\n",
        "$$w_0^{(1)} + w_1^{(1)} \\, x_1 + w_2^{(1)} \\, x_2 + w_3^{(1)} \\, x_3 + w_4^{(1)} \\, x_4 $$\n",
        "\n",
        "in the above example.\n",
        "\n",
        "Putting everything together, the three outputs of the first hidden layer are:\n",
        "\n",
        "$$\n",
        "\t {\\rm ReLu} \\left(w_0^{(1)} + w_1^{(1)} \\, x_1 + w_2^{(1)} \\, x_2 + w_3^{(1)} \\, x_3 + w_4^{(1)} \\, x_4 \\right)  \\\\\n",
        "   {\\rm ReLu} \\left(w_0^{(2)} + w_1^{(2)} \\, x_1 + w_2^{(2)} \\, x_2 + w_3^{(2)} \\, x_3 + w_4^{(2)} \\, x_4 \\right)  \\\\\n",
        " {\\rm ReLu} \\left(w_0^{(3)} + w_1^{(3)} \\, x_1 + w_2^{(3)} \\, x_2 + w_3^{(3)} \\, x_3 + w_4^{(3)} \\, x_4 \\right)  \\\\\n",
        "$$\n",
        "\n",
        "Then, calculations proceed to the following layer, and so on, until they reach  the output layer. This network is called *feed-forward* because computations are done sequentially layer by layer.\n",
        "\n"
      ],
      "metadata": {
        "id": "LVVVxdMRMEyV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Techniques to improve deep learning"
      ],
      "metadata": {
        "id": "CTkkRiF4A9TH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Regularization** is a technique used in machine learning to prevent overfitting by adding a penalty term to the loss function. This encourages the model to learn a simpler representation of the data and reduces its capacity to memorize the training data.\n",
        "\n",
        "**Self-regularized activation functions** can help improve the generalization performance of a neural network by introducing an implicit form of regularization. This can be achieved through various mechanisms, such as controlling the distribution of the activations or the gradients. For example, the *Mish activation function* has been shown to have a self-regularizing effect due to its non-monotonic and smooth nature, which can help prevent the vanishing gradient problem and improve the training dynamics of deep neural networks.\n",
        "\n",
        "The *Mish activation function* (https://arxiv.org/abs/1908.08681) is an alternative to *ReLu*. It is a smooth, continuous, self regularized, non-monotonic activation function mathematically defined as\n",
        "\n",
        "$$f(x)= x \\, {\\rm tanh} (\\ln (1+e^x)).$$\n",
        "\n",
        "**Dropout** is a regularization technique used in deep learning to prevent overfitting. It works by randomly “dropping out” or deactivating some of the neurons in a neural network during training. This means that during each forward pass, some of the neurons are temporarily removed from the network, along with all their incoming and outgoing connections.\n",
        "\n",
        "The idea behind dropout is to introduce randomness and prevent the model from relying too heavily on any single neuron or feature. By randomly dropping out neurons during training, the model is forced to learn a more robust representation of the data that is less sensitive to small changes in the input.\n",
        "\n",
        "Dropout is typically applied to the hidden layers of a neural network and can be controlled by a hyperparameter called the dropout rate, which specifies the probability that any given neuron will be dropped out during training. A common value for the dropout rate is 0.5, meaning that on average, half of the neurons in a given layer will be dropped out during each forward pass.\n",
        "\n",
        "During testing or inference, dropout is not applied and all neurons are active. However, to account for the fact that only a fraction of the neurons were active during training, the outputs of the neurons are typically scaled down by the dropout rate.\n",
        "\n",
        "**Momentum**  is a technique used in deep learning to accelerate the training of neural networks. It is an optimization algorithm that helps the model converge faster by adding a fraction of the previous weight update to the current weight update.\n",
        "\n",
        "In gradient descent, the weights of a neural network are updated by taking a step in the direction of the negative gradient of the loss function with respect to the weights. This can sometimes result in slow convergence or getting stuck in local minima. Momentum addresses these issues by introducing a “momentum” term that takes into account the previous weight updates.\n",
        "\n",
        "The idea behind momentum is to add a fraction of the previous weight update to the current weight update, effectively “smoothing out” the updates and helping the model converge faster. This can be controlled by a hyperparameter called the momentum coefficient, which specifies how much of the previous weight update should be added to the current weight update. A common value for the momentum coefficient is 0.9.\n",
        "\n",
        "Momentum can be used with various optimization algorithms, such as stochastic gradient descent (SGD) or Adam, to improve their convergence properties.\n",
        "\n",
        "**Adam** (short for Adaptive Moment Estimation) is an optimization algorithm commonly used in deep learning to train neural networks. It is an extension of stochastic gradient descent (SGD) that incorporates ideas from other optimization algorithms such as AdaGrad and RMSProp.\n",
        "\n",
        "Adam works by maintaining an estimate of the first and second moments of the gradients (i.e., the mean and uncentered variance) and using these estimates to adaptively adjust the learning rate for each weight in the network. This allows the algorithm to converge faster and achieve better performance than traditional SGD. For details, look at the [pseudo-code for Adam](https://pytorch.org/docs/stable/generated/torch.optim.Adam.html).\n",
        "\n",
        "One of the key advantages of Adam is that it requires little tuning of its hyperparameters. The algorithm has three main hyperparameters: the learning rate, the first moment decay rate (beta1), and the second moment decay rate (beta2). The default values for these hyperparameters (0.001, 0.9, and 0.999, respectively) usually work well in practice. Adam has been shown to work well on a wide range of deep learning problems and is often used as the default optimizer in many deep learning frameworks.\n"
      ],
      "metadata": {
        "id": "rYJGaxwxBEMG"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HarhfRxO7shD"
      },
      "source": [
        "**Batch normalization**  tries to maintain a good distribution of activations throughout training. The paper [\"Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift\"](https://arxiv.org/abs/1502.03167) addresses the realization that training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change, which slows down training.\n",
        "\n",
        "That problem, known as *internal covariate shift* can be addressed by normalizing layer inputs. Details of implementation can be found at [PyTorch documentation](https://pytorch.org/docs/stable/generated/torch.nn.functional.batch_norm.html).\n",
        "\n",
        "The follownig code illustrates, for the CIFAR-10 data set (32$\\times$32 color images) the use of `BatchNorm` in PyTorch to create a NN model.\n",
        "\n",
        "```\n",
        "nn.Sequential(\n",
        "      nn.Flatten(),\n",
        "      nn.Linear(32 * 32 * 3, 64),\n",
        "      nn.BatchNorm1d(64),\n",
        "      nn.ReLU(),\n",
        "      nn.Linear(64, 32),\n",
        "      nn.BatchNorm1d(32),\n",
        "      nn.ReLU(),\n",
        "      nn.Linear(32, 10)\n",
        "    )\n",
        "```\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**TensorBoard** is a tool for providing the measurements and visualizations needed during the machine learning workflow. It enables tracking experiment metrics like loss and accuracy, visualizing the model graph, projecting embeddings to a lower dimensional space, and much more. See this  [Colab notebook that uses tensorboard with Keras](https://colab.research.google.com/github/tensorflow/tensorboard/blob/master/docs/tensorboard_in_notebooks.ipynb)"
      ],
      "metadata": {
        "id": "sM6vNeVpCRRQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Example of NN classifier implemented with PyTorch"
      ],
      "metadata": {
        "id": "QLwAmlJC-GhY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "`PyTorch` provides the designed modules and classes `torch.nn` , `torch.optim` , `Dataset` , and `DataLoader` to help you create and train neural networks. On their webpage, you can find a broad range of tutorials [https://pytorch.org/tutorials/](https://pytorch.org/tutorials/) and, in particular, on [`torch.nn`](https://pytorch.org/tutorials/beginner/nn_tutorial.html).\n",
        "\n",
        "The following script creates a $n$-layer neural network with `PyTorch` and applies it to some available dataset (`iris` or the 8$\\times$8 MNIST digit dataset). The script contains many parameters that have been discussed above, namely:\n",
        "- architecture of the neural network;\n",
        "- batch size;\n",
        "- number of epochs\n",
        "- learning rate;\n",
        "- regularization parameter;\n",
        "- momentum;\n",
        "- dropout proportion.\n",
        "\n",
        "The script illustrates how to create a dataloader in `PyTorch` which makes it easy to loop through mini-batches while training the model. It also plots train and test loss along epochs. This is useful to choose the best number of epochs to train the model and avoid overfitting.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "M3Ofg2i5-QHv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script that implements a neural network with PyTorch (over the iris or mnist datasets)\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "from torch.utils.data import DataLoader, TensorDataset\n",
        "from sklearn.datasets import load_iris, load_digits\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import accuracy_score, confusion_matrix, ConfusionMatrixDisplay\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "import numpy as np\n",
        "\n",
        "CREATE_CLASS=True # Create class from scratch; otherwise use nn.Sequential to create the class\n",
        "SGD=False # SGD or Adam\n",
        "IRIS=False # iris or mnist\n",
        "SHOW=False # returns picture of digit for mnist\n",
        "\n",
        "# Load Iris dataset\n",
        "if IRIS:\n",
        "    examples = load_iris()\n",
        "else:\n",
        "    examples = load_digits() # https://scikit-learn.org/stable/auto_examples/classification/plot_digits_classification.html; 10 digits;  1797 examples\n",
        "    if SHOW:\n",
        "        idx=random.randint(0,len(examples.target))\n",
        "        print(examples.data[idx])\n",
        "        print(examples.data[idx].reshape(8,8))\n",
        "        print(examples.target[idx])\n",
        "        plt.matshow(examples.data[idx].reshape(8,8), cmap=plt.cm.gray_r)\n",
        "        plt.show()\n",
        "\n",
        "X = examples.data\n",
        "y = examples.target\n",
        "\n",
        "# Splitting data into train and test sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
        "\n",
        "# Standardize features\n",
        "scaler = StandardScaler()\n",
        "X_train = scaler.fit_transform(X_train)\n",
        "X_test = scaler.transform(X_test)\n",
        "\n",
        "# Convert numpy arrays to PyTorch tensors\n",
        "X_train_tensor = torch.tensor(X_train, dtype=torch.float32)\n",
        "X_test_tensor = torch.tensor(X_test, dtype=torch.float32)\n",
        "y_train_tensor = torch.tensor(y_train, dtype=torch.long)\n",
        "y_test_tensor = torch.tensor(y_test, dtype=torch.long)\n",
        "\n",
        "# Instantiate the model\n",
        "input_size = X_train_tensor.shape[1]\n",
        "hidden_size = 8\n",
        "output_size = len(examples.target_names)\n",
        "batch_size=400\n",
        "num_epochs = 200\n",
        "# Optimizer specific options\n",
        "learning_rate=0.1\n",
        "regularization_param=0.001\n",
        "momentum_param=0.9\n",
        "# Dropout: if p>0\n",
        "dropout_p=0.25 # During training, randomly zeroes some of the elements of the input tensor with probability p.\n",
        "\n",
        "# Create dataloader which makes it easier to use mini batches\n",
        "train_dl=DataLoader(TensorDataset(X_train_tensor,y_train_tensor), batch_size, shuffle=True)\n",
        "\n",
        "########################################################### NN model\n",
        "if CREATE_CLASS:\n",
        "    # Create model, first defining the class with a forward method\n",
        "    class ThreeLayerNet(nn.Module):\n",
        "        def __init__(self, input_size, hidden_size, output_size):\n",
        "            super(ThreeLayerNet, self).__init__()\n",
        "            self.fc1 = nn.Linear(input_size, hidden_size)\n",
        "            self.fc2 = nn.Linear(hidden_size, hidden_size)\n",
        "            self.fc3 = nn.Linear(hidden_size, output_size)\n",
        "            self.dropout = nn.Dropout(p=dropout_p)  # Dropout layer with dropout probability\n",
        "        def forward(self, x):\n",
        "            x = torch.relu(self.fc1(x))\n",
        "            x = self.dropout(x)  # Apply dropout after first hidden layer\n",
        "            x = torch.relu(self.fc2(x))\n",
        "            x = self.dropout(x)  # Apply dropout after second hidden layer\n",
        "            x = self.fc3(x)\n",
        "            return x\n",
        "    model = ThreeLayerNet(input_size, hidden_size, output_size)\n",
        "else:\n",
        "    # Or, in alternative, use nn.Sequential\n",
        "    model=nn.Sequential(\n",
        "        nn.Linear(input_size, hidden_size),\n",
        "        nn.ReLU(),\n",
        "        nn.Dropout(p=dropout_p),\n",
        "        nn.Linear(hidden_size, hidden_size),\n",
        "        nn.ReLU(),\n",
        "        nn.Dropout(p=dropout_p),\n",
        "        nn.Linear(hidden_size, output_size)\n",
        "    )\n",
        "####################################################################################################\n",
        "# Define loss function and optimizer\n",
        "# Either torch.nn.NLLLoss or torch.nn.CrossEntropyLoss can be used: CrossEntropyLoss (https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html) implements softmax internally\n",
        "criterion = nn.CrossEntropyLoss() #\n",
        "# Optimizer: optimizer object that will hold the current state and will update the parameters based on the computed gradients\n",
        "# for param in model.parameters(): print(param.data)\n",
        "if SGD:\n",
        "    optimizer = optim.SGD(model.parameters(), lr=learning_rate, weight_decay=regularization_param, momentum=momentum_param)\n",
        "else:\n",
        "    optimizer = optim.Adam(model.parameters(), lr=learning_rate, weight_decay=regularization_param)\n",
        "\n",
        "# Lists to store train and test losses\n",
        "train_losses = []\n",
        "test_losses = []\n",
        "\n",
        "# Training the model\n",
        "for epoch in range(num_epochs):\n",
        "    model.train()\n",
        "    train_loss = 0.0\n",
        "    for x_batch, y_batch in train_dl:\n",
        "        # Forward pass\n",
        "        pred = model(x_batch) # Returns tensor: nrows=tensor batch_size; ncols=number of classes\n",
        "        loss = criterion(pred, y_batch)\n",
        "\n",
        "        # Backward pass and optimization\n",
        "        optimizer.zero_grad() # Resets the gradients of all optimized tensors\n",
        "        loss.backward() # Computes gradient\n",
        "        optimizer.step() # Performs a single optimization step (parameter update).\n",
        "\n",
        "        train_loss += loss.item() # .item() extracts the scalar value of the loss tensor\n",
        "\n",
        "    train_loss /= len(train_dl)\n",
        "    train_losses.append(train_loss)\n",
        "\n",
        "    # Test the model\n",
        "    # We also put the model in evaluation mode, so that specific layers\n",
        "    # such as dropout or batch normalization layers behave correctly.\n",
        "    model.eval()\n",
        "    with torch.no_grad():\n",
        "        outputs = model(X_test_tensor)\n",
        "        test_loss = criterion(outputs, y_test_tensor)\n",
        "        test_losses.append(test_loss.item())\n",
        "\n",
        "    if (epoch+1) % 100 == 0:\n",
        "        print(f'Epoch [{epoch+1}/{num_epochs}], Train Loss: {train_loss:.4f}, Test Loss: {test_loss:.4f}')\n",
        "\n",
        "# Plotting train and test losses\n",
        "plt.plot(range(num_epochs), train_losses, label='Train Loss')\n",
        "plt.plot(range(num_epochs), test_losses, label='Test Loss')\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Loss')\n",
        "plt.title('Train and Test Losses')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Testing the model\n",
        "with torch.no_grad():\n",
        "    outputs = model(X_test_tensor)\n",
        "    _, predicted = torch.max(outputs, 1) # Returns a namedtuple (values, indices) where values is the maximum value of each row of the input tensor in the given dimension dim. And indices is the index location of each maximum value found (argmax).\n",
        "\n",
        "actual=y_test_tensor.numpy()\n",
        "pred=predicted.numpy()\n",
        "accuracy = accuracy_score(actual, pred)\n",
        "print(f'Accuracy on test set: {accuracy:.4f}')\n",
        "cm=confusion_matrix(actual, pred)\n",
        "labels = np.unique(actual)\n",
        "disp = ConfusionMatrixDisplay(confusion_matrix=cm, display_labels=labels)\n",
        "disp.plot()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 956
        },
        "id": "PFVbrMpWCOLY",
        "outputId": "0cebc971-4ef1-4ad4-c0a9-e918ddfe5b79"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch [100/200], Train Loss: 0.8591, Test Loss: 0.3878\n",
            "Epoch [200/200], Train Loss: 0.8437, Test Loss: 0.4352\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy on test set: 0.8833\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Improved (more modular) script that implements a neural network with PyTorch over the mnist 8 by 8 practice data set\n",
        "# code adapted from https://github.com/rasbt/machine-learning-book/blob/main/ch14/ch14_part1.py\n",
        "\n",
        "'''\n",
        "This code does the following:\n",
        "    Splits the dataset into training and testing sets.\n",
        "    Standardizes the features using StandardScaler.\n",
        "    Reshapes dataset to fit the model\n",
        "    Instantiates the model (NN)\n",
        "    Defines the loss function (Cross Entropy Loss) and optimizer (Adam).\n",
        "    Trains the model for num_epochs epochs.\n",
        "    Tests the trained model on the test set and evaluates the accuracy.\n",
        "'''\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "from torchsummary import summary\n",
        "from torch.utils.data import DataLoader, TensorDataset\n",
        "from sklearn.datasets import load_digits # https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_digits.html\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import ConfusionMatrixDisplay\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "import numpy as np\n",
        "\n",
        "########################################################################### my functions\n",
        "\n",
        "def train(model, optimizer, loss_fn, num_epochs, train_dl, valid_dl):\n",
        "    '''\n",
        "    Main function to train and test the model\n",
        "    '''\n",
        "    # lists to strore losses and accuracies\n",
        "    loss_hist_train = [0] * num_epochs\n",
        "    accuracy_hist_train = [0] * num_epochs\n",
        "    loss_hist_valid = [0] * num_epochs\n",
        "    accuracy_hist_valid = [0] * num_epochs\n",
        "    # main loop through epochs\n",
        "    for epoch in range(num_epochs):\n",
        "        # training mode\n",
        "        model.train()\n",
        "        for x_batch, y_batch in train_dl:\n",
        "            # core of the learning process: predict and fit\n",
        "            pred = model(x_batch)\n",
        "            loss = loss_fn(pred, y_batch)\n",
        "            loss.backward()\n",
        "            optimizer.step()\n",
        "            optimizer.zero_grad()\n",
        "            # compute train loss and accuracy\n",
        "            loss_hist_train[epoch] += loss.item()*y_batch.size(0)\n",
        "            is_correct = (torch.argmax(pred, dim=1) == y_batch).float()\n",
        "            accuracy_hist_train[epoch] += is_correct.sum()\n",
        "        # compute average loss per epoch\n",
        "        loss_hist_train[epoch] /= len(train_dl.dataset)\n",
        "        accuracy_hist_train[epoch] /= len(train_dl.dataset)\n",
        "        # we also put the model in evaluation mode, so that specific layers such as dropout or batch normalization layers behave correctly.\n",
        "        model.eval()\n",
        "        with torch.no_grad():\n",
        "            for x_batch, y_batch in valid_dl:\n",
        "                # predict\n",
        "                pred = model(x_batch)\n",
        "                loss = loss_fn(pred, y_batch)\n",
        "                loss_hist_valid[epoch] += loss.item()*y_batch.size(0)\n",
        "                is_correct = (torch.argmax(pred, dim=1) == y_batch).float()\n",
        "                accuracy_hist_valid[epoch] += is_correct.sum()\n",
        "                if epoch==0:\n",
        "                    preds,actuals=torch.argmax(pred, dim=1),y_batch\n",
        "                else:\n",
        "                    preds=torch.cat((preds,torch.argmax(pred, dim=1)),dim=0)\n",
        "                    actuals=torch.cat((actuals,y_batch),dim=0)\n",
        "        # compute average loss per epoch\n",
        "        loss_hist_valid[epoch] /= len(valid_dl.dataset)\n",
        "        accuracy_hist_valid[epoch] /= len(valid_dl.dataset)\n",
        "        # print accuracy\n",
        "        if (epoch+1) % 100==0:\n",
        "            print(f'Epoch {epoch+1} accuracy: {accuracy_hist_train[epoch]:.4f} val_accuracy: {accuracy_hist_valid[epoch]:.4f}')\n",
        "    return loss_hist_train, loss_hist_valid, accuracy_hist_train, accuracy_hist_valid, preds,actuals\n",
        "\n",
        "\n",
        "def plot_accuracy_from_predictions(hist):\n",
        "    ''' Creates and prints confusion matrix from a model and a set of examples\n",
        "    Inputs\n",
        "    ------\n",
        "    hist: tuple\n",
        "        where hist[4] is the list of predicted values for test and hist[5] are the actual labels\n",
        "    '''\n",
        "    pred=hist[4].numpy()\n",
        "    actual=hist[5].numpy()\n",
        "    labels = np.unique(actual)\n",
        "    disp = ConfusionMatrixDisplay.from_predictions(actual,pred,labels=labels)\n",
        "    # print global accuracy\n",
        "    accuracy=np.sum(np.diagonal(disp.confusion_matrix))/np.sum(disp.confusion_matrix)\n",
        "    print(f'Accuracy on test set: {accuracy:.4f}')\n",
        "    plt.show()\n",
        "\n",
        "def plot_losses(hist):\n",
        "    ''' plots train and test loss\n",
        "    Input\n",
        "    ------\n",
        "    history, the output of function train()\n",
        "    '''\n",
        "    x_arr = np.arange(len(hist[0])) + 1\n",
        "    fig = plt.figure(figsize=(12, 4))\n",
        "    ax = fig.add_subplot(1, 2, 1)\n",
        "    ax.plot(x_arr, hist[0], '-o', label='Train loss')\n",
        "    ax.plot(x_arr, hist[1], '--<', label='Test loss')\n",
        "    ax.set_xlabel('Epoch', size=15)\n",
        "    ax.set_ylabel('Loss', size=15)\n",
        "    ax.legend(fontsize=15)\n",
        "    ax = fig.add_subplot(1, 2, 2)\n",
        "    ax.plot(x_arr, hist[2], '-o', label='Train acc.')\n",
        "    ax.plot(x_arr, hist[3], '--<', label='Test acc.')\n",
        "    ax.legend(fontsize=15)\n",
        "    ax.set_xlabel('Epoch', size=15)\n",
        "    ax.set_ylabel('Accuracy', size=15)\n",
        "    plt.show()\n",
        "\n",
        "################################################################################ Data and parameters\n",
        "\n",
        "SHOW=False # returns picture of a randomly chosen digit\n",
        "\n",
        "examples = load_digits() # https://scikit-learn.org/stable/auto_examples/classification/plot_digits_classification.html; 10 digits;  1797 examples\n",
        "if SHOW:\n",
        "    idx=random.randint(0,len(examples.target))\n",
        "    print(examples.data[idx])\n",
        "    print(examples.data[idx].reshape(8,8))\n",
        "    print(examples.target[idx])\n",
        "    plt.matshow(examples.data[idx].reshape(8,8), cmap=plt.cm.gray_r)\n",
        "    plt.show()\n",
        "\n",
        "X = examples.data # np.ndarray (1797, 64)\n",
        "y = examples.target # (1797,)\n",
        "\n",
        "# parameter constants\n",
        "test_size=0.2\n",
        "hidden_size = 8\n",
        "batch_size= 256\n",
        "num_epochs = 50\n",
        "# Optimizer specific options\n",
        "learning_rate=0.1\n",
        "regularization_param=0.001\n",
        "# Dropout: if p>0\n",
        "dropout_p=0.1 # During training, randomly zeroes some of the elements of the input tensor with probability p.\n",
        "\n",
        "########################################################################### train and test, pre-processing\n",
        "# Splitting data into train and test sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=test_size, random_state=42)\n",
        "\n",
        "# Standardize features\n",
        "scaler = StandardScaler()\n",
        "X_train = scaler.fit_transform(X_train)\n",
        "X_test = scaler.transform(X_test)\n",
        "\n",
        "# Convert numpy arrays to PyTorch tensors\n",
        "X_train_tensor = torch.tensor(X_train, dtype=torch.float32)\n",
        "X_test_tensor = torch.tensor(X_test, dtype=torch.float32)\n",
        "y_train_tensor = torch.tensor(y_train, dtype=torch.long)\n",
        "y_test_tensor = torch.tensor(y_test, dtype=torch.long)\n",
        "print('Number of examples in training set:',X_train_tensor.shape)\n",
        "print('Number of examples in test set:', X_test_tensor.shape)\n",
        "\n",
        "# Instantiate the model\n",
        "input_size = X_train_tensor.shape[1]\n",
        "output_size = len(examples.target_names)\n",
        "\n",
        "# Create dataloader with batch_size\n",
        "train_dl=DataLoader(TensorDataset(X_train_tensor,y_train_tensor), batch_size, shuffle=True)\n",
        "test_dl=DataLoader(TensorDataset(X_test_tensor,y_test_tensor), batch_size, shuffle=False)\n",
        "\n",
        "###################################################################################### NN model\n",
        "model=nn.Sequential(\n",
        "    nn.Linear(input_size, hidden_size),\n",
        "    nn.BatchNorm1d(hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Dropout(p=dropout_p),\n",
        "    nn.Linear(hidden_size, hidden_size),\n",
        "    nn.BatchNorm1d(hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Dropout(p=dropout_p),\n",
        "    nn.Linear(hidden_size, output_size)\n",
        ")\n",
        "\n",
        "# Define loss function and optimizer\n",
        "# Either torch.nn.NLLLoss or torch.nn.CrossEntropyLoss can be used: CrossEntropyLoss (https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html) implements softmax internally\n",
        "loss_fn = nn.CrossEntropyLoss()\n",
        "\n",
        "# Optimizer: optimizer object that will hold the current state and will update the parameters based on the computed gradients\n",
        "# for param in model.parameters(): print(param.data)\n",
        "optimizer = optim.Adam(model.parameters(), lr=learning_rate, weight_decay=regularization_param)\n",
        "\n",
        "# Train the model and predict on test samples to estimate accuracy\n",
        "# history stores losses, accuracy, actual labels and predictions\n",
        "history = train(model, optimizer, loss_fn, num_epochs, train_dl, test_dl)\n",
        "\n",
        "# plot losses along epochs\n",
        "plot_losses(history)\n",
        "# plot confusion matrix\n",
        "plot_accuracy_from_predictions(history)\n",
        "#plot_accuracy(hist)"
      ],
      "metadata": {
        "id": "rBFfDrHi63JM",
        "outputId": "4ad6f5cc-2fba-4805-9096-e653aa8ae8e9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 878
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of examples in training set: torch.Size([1437, 64])\n",
            "Number of examples in test set: torch.Size([360, 64])\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy on test set: 0.9125\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Image classification"
      ],
      "metadata": {
        "id": "6mQQM1QvFPZ-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Image classification applies a class label to an entire image. For example, a simple image classification model might be trained to categorize photographs of crops into their category as in https://www.kaggle.com/datasets/mdwaquarazam/agricultural-crops-image-classification.\n",
        "\n",
        "\n",
        "Convolutional neural networks (CNN) are the main machine learning models for image classification. They use image filters (aka covolutions) similarly to conventional image processing techniques to extract features from the images. However, CNN  are trained to determine their own image filters from examples. This is unlike the conventional approach where filters have to be carefully coded and are domain specific.\n",
        "\n"
      ],
      "metadata": {
        "id": "1yIjopNB75t9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Convolutions and kernels"
      ],
      "metadata": {
        "id": "HPga1DGR_h4S"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Note: For a detailed overview of convolutional neural networks see the notebook that includes `pytorch`code for computing convolutions:  https://github.com/fastai/fastbook/blob/master/13_convolutions.ipynb. Some concepts and examples from that notebook are included in the text below. For a friendly introduction to convolutions with nice animations, consider watching  the video [https://www.3blue1brown.com/lessons/convolutions](https://www.3blue1brown.com/lessons/convolutions).\n",
        "\n",
        "A convolution applies a kernel across an image. A kernel is a little matrix, such as the 3×3 matrix below. The 7×7 grid to the left is the image we're going to apply the kernel to. The convolution operation multiplies each element of the kernel by each element of a 3×3 block of the image. The results of these multiplications are then added together. The diagram  shows an example of applying a kernel to a single location in the image, the 3×3 block around cell 18."
      ],
      "metadata": {
        "id": "De9r08q58Jf_"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Pm9ZH_4P7sgM"
      },
      "source": [
        "<img src=\"https://github.com/fastai/fastbook/blob/master/images/chapter9_conv_basic.png?raw=1\" id=\"basic_conv\" caption=\"Applying a kernel to one location\" alt=\"Applying a kernel to one location\" width=\"600\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HytpwvII7sga"
      },
      "source": [
        "In the paper [\"A Guide to Convolution Arithmetic for Deep Learning\"](https://arxiv.org/abs/1603.07285) there are many great diagrams showing how image kernels can be applied. Here's an example from the paper showing (at the bottom) a light blue 4×4 image, with a dark blue 3×3 kernel being applied, creating a 2×2 green output activation map at the top."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fM0gl8pN7sga"
      },
      "source": [
        "<img alt=\"Result of applying a 3×3 kernel to a 4×4 image\" width=\"782\" caption=\"Result of applying a 3×3 kernel to a 4×4 image (courtesy of Vincent Dumoulin and Francesco Visin)\" id=\"three_ex_four_conv\" src=\"https://github.com/fastai/fastbook/blob/master/images/att_00028.png?raw=1\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YZTVi15h7sga"
      },
      "source": [
        "What is the shape of the result? If the original image has a height of `h` and a width of `w`, how many 3×3 windows can we find? As you can see from the example, there are `h-2` by `w-2` windows, so the image we get has a result as a height of `h-2` and a width of `w-2`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gx_3HUel_N6i"
      },
      "source": [
        "#### Padding, pooling, stride and activation map"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Feature map** (aka **activation map**) is the output of the application of the filter to some input image (which can be either the raw input image or some feature map) as illustrated in the figures above. The name *feature map* stresses the fact that convolution creates (or extracts) new features from some image. The name *activation map* (not to be confounded with the *activation function* of NNs) stresses that the high values in the output correspond to  parts of the input image that are activated by the convolution operation."
      ],
      "metadata": {
        "id": "_CERU-wO5KM1"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bhvgNqbz_N6j"
      },
      "source": [
        "**Padding** consists in creating new cells on the margins of the input, with a given value (in general 0). With appropriate padding, we can ensure that the output **activation map** is the same size as the original image, which can make things a lot simpler when we construct our architectures. The figure below shows how adding padding allows us to apply the kernels in the image corners."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EwuyrTB3_N6j"
      },
      "source": [
        "<img src=\"https://github.com/fastai/fastbook/blob/master/images/chapter9_padconv.svg?raw=1\" id=\"pad_conv\" caption=\"A convolution with padding\" alt=\"A convolution with padding\" width=\"600\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uBonLNgi_N6k"
      },
      "source": [
        "With a 5×5 input, 4×4 kernel, and 2 pixels of padding, we end up with a 6×6 activation map:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IZs6pyQO_N6k"
      },
      "source": [
        "<img alt=\"A 4×4 kernel with 5×5 input and 2 pixels of padding\" width=\"783\" caption=\"A 4×4 kernel with 5×5 input and 2 pixels of padding (courtesy of Vincent Dumoulin and Francesco Visin)\" id=\"four_by_five_conv\" src=\"https://github.com/fastai/fastbook/blob/master/images/att_00029.png?raw=1\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jBr61m-P_N6l"
      },
      "source": [
        "If we apply to some image a kernel of size `ks` by `ks` (with `ks` an odd number), the necessary padding on each side to keep the same shape is `ks//2`. An even number for `ks` would require a different amount of padding on the top/bottom and left/right, but in practice we almost never use an even filter size.\n",
        "\n",
        "**Stride**. So far, when we have applied the kernel to the grid, we have moved it one pixel over at a time. But we can jump further; for instance, we could move over two pixels after each kernel application, as in the figure below. This is known as a *stride-2* convolution and will reduce the size in the example from 5$\\times$5 to 3$\\times$3.\n",
        "\n",
        "In short, **stride-2** convolutions are useful for decreasing the size of our outputs, and **stride-1** convolutions (with padding) are useful for adding layers while preserving the image size."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T1cu9Gle_N6m"
      },
      "source": [
        "<img alt=\"A 3×3 kernel with 5×5 input, stride-2 convolution, and 1 pixel of padding\" width=\"774\" caption=\"A 3×3 kernel with 5×5 input, stride-2 convolution, and 1 pixel of padding (courtesy of Vincent Dumoulin and Francesco Visin)\" id=\"three_by_five_conv\" src=\"https://github.com/fastai/fastbook/blob/master/images/att_00030.png?raw=1\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dFr3YGMP_N6m"
      },
      "source": [
        "In general, if the input image has size `h` $\\times$ `w`, using a padding of 1 and a stride of 2 (as in the example above) will output an image of size `(h+1)//2` $\\times$  `(w+1)//2`. The general formula for each dimension is `(n + 2*pad - ks)//stride + 1`, where `pad` is the padding, `ks`, the size of our kernel, and `stride` is the stride.\n",
        "\n",
        "**Pooling** is a type of convolution with a fixed operation (not trainable) as illustrated in the example below. This can be used to reduce the size of a layer. However, pooling can be replaced by convolution with stride larger than 1 (see paper \"Striving for Simplicity: The All Convolutional Net\" at https://arxiv.org/abs/1412.6806).\n",
        "\n",
        "<img src=\"https://epynn.net/_images/pool-01.svg\"  width=\"600\">\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we apply the operations described above to create a convolutional neural network. To that end, we adapt the script that implemented a neural network for classifying the examples in the 8$\\times$8 MNIST data set.\n",
        "\n",
        "We re-use all the auxiliary functions `train` (main function for training the neural network), `plot_accuracy_from_predictions` and `plot_losses`from the previous script. There are two main changes:\n",
        "1. Additional pre-processing is need to reshape the examples to NCHW (batch size, channels, height and width);  \n",
        "2. The model is expanded with *2D-convolutional* and *maxpool* layers.\n",
        "\n",
        "You need to run the previous NN script first to define the auxiliary functions that this script uses."
      ],
      "metadata": {
        "id": "wizsHEfDNC48"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script that implements a convolutional neural network with PyTorch over the mnist 8 by 8 practice data set\n",
        "# code adapted from https://github.com/rasbt/machine-learning-book/blob/main/ch14/ch14_part1.py\n",
        "\n",
        "'''\n",
        "This code does the following:\n",
        "    Splits the dataset into training and testing sets.\n",
        "    Standardizes the features using StandardScaler.\n",
        "    Reshapes dataset to fit the model\n",
        "    Instantiates the model (CNN)\n",
        "    Defines the loss function (Cross Entropy Loss) and optimizer (Adam).\n",
        "    Trains the model for num_epochs epochs.\n",
        "    Tests the trained model on the test set and evaluates the accuracy.\n",
        "'''\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "from torchsummary import summary\n",
        "from torch.utils.data import DataLoader, TensorDataset\n",
        "from sklearn.datasets import  load_digits\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import ConfusionMatrixDisplay\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "import numpy as np\n",
        "\n",
        "################################################################################ Data and parameters\n",
        "SHOW=False # plot some digit for mnist 8*8\n",
        "\n",
        "examples = load_digits() # https://scikit-learn.org/stable/auto_examples/classification/plot_digits_classification.html; 10 digits;  1797 examples\n",
        "if SHOW:\n",
        "    idx=random.randint(0,len(examples.target))\n",
        "    print(examples.data[idx])\n",
        "    print(examples.data[idx].reshape(8,8))\n",
        "    print(examples.target[idx])\n",
        "    plt.matshow(examples.data[idx].reshape(8,8), cmap=plt.cm.gray_r)\n",
        "    plt.show()\n",
        "\n",
        "X = examples.data # np.ndarray (1797, 64)\n",
        "y = examples.target # (1797,)\n",
        "\n",
        "# parameter constants\n",
        "test_size=0.2\n",
        "hidden_size = 8\n",
        "batch_size= 256\n",
        "num_epochs = 50\n",
        "# Optimizer specific options\n",
        "learning_rate=0.1\n",
        "regularization_param=0.001\n",
        "# Dropout: if p>0\n",
        "dropout_p=0.1 # During training, randomly zeroes some of the elements of the input tensor with probability p.\n",
        "\n",
        "########################################################################### train and test, pre-processing\n",
        "# Splitting data into train and test sets\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=test_size, random_state=42)\n",
        "\n",
        "# Standardize features\n",
        "scaler = StandardScaler()\n",
        "print(X_train.shape)\n",
        "X_train = scaler.fit_transform(X_train)\n",
        "X_test = scaler.transform(X_test)\n",
        "\n",
        "# mnist data set has examples with 64 attributes\n",
        "# We need to reshape that information into NCHW (batch size, channels, height, width)\n",
        "def reshape_mnist(X,W,H):\n",
        "    X=X.reshape((X.shape[0],W,H))\n",
        "    return np.expand_dims(X,1) # one channel\n",
        "\n",
        "# Convert numpy arrays to PyTorch tensors of the right shape (labels do not need to be reshaped)\n",
        "X_train_tensor = torch.tensor(reshape_mnist(X_train,8,8), dtype=torch.float32)\n",
        "X_test_tensor = torch.tensor(reshape_mnist(X_test,8,8), dtype=torch.float32)\n",
        "y_train_tensor = torch.tensor(y_train, dtype=torch.long)\n",
        "y_test_tensor = torch.tensor(y_test, dtype=torch.long)\n",
        "print('Number of examples in training set:',X_train_tensor.shape)\n",
        "print('Number of examples in test set:', X_test_tensor.shape)\n",
        "\n",
        "# Instantiate the model\n",
        "input_size = X_train_tensor.shape[1]\n",
        "output_size = len(examples.target_names)\n",
        "\n",
        "# Create dataloader and determine batch size (note: batchsize is the first parameter in NCHW)\n",
        "train_dl=DataLoader(TensorDataset(X_train_tensor,y_train_tensor), batch_size, shuffle=True)\n",
        "test_dl=DataLoader(TensorDataset(X_test_tensor,y_test_tensor), batch_size, shuffle=True)\n",
        "\n",
        "if SHOW:\n",
        "    class_names = [str(i) for i in range(10)]\n",
        "    # Plot the images\n",
        "    plt.figure(figsize=(10, 5))\n",
        "    image_count = 0\n",
        "    for images, labels in train_dl:\n",
        "        for i in range(len(images)):\n",
        "            plt.subplot(4, 5, image_count + 1)\n",
        "            plt.imshow(np.transpose(images[i], (1, 2, 0)), cmap=\"gray\")\n",
        "            plt.title(class_names[labels[i]])\n",
        "            plt.axis('off')\n",
        "            image_count += 1\n",
        "            if image_count >= 20:\n",
        "                break\n",
        "        if image_count >= 20:\n",
        "            break\n",
        "    plt.show()\n",
        "\n",
        "###################################################################################### CNN  model\n",
        "model=nn.Sequential(\n",
        "    nn.Conv2d(in_channels=1,out_channels=8,kernel_size=3,padding=1),\n",
        "    nn.ReLU(),\n",
        "    nn.MaxPool2d(kernel_size=2),\n",
        "    nn.Flatten(),\n",
        "    nn.Linear(8*4*4, hidden_size),\n",
        "    nn.BatchNorm1d(hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(hidden_size, hidden_size),\n",
        "    nn.BatchNorm1d(hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Dropout(p=dropout_p),\n",
        "    nn.Linear(hidden_size, output_size)\n",
        ")\n",
        "\n",
        "'''\n",
        "Compare with NN from previous script:\n",
        "model=nn.Sequential(\n",
        "    nn.Linear(input_size, hidden_size),\n",
        "    nn.BatchNorm1d(hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Dropout(p=dropout_p),\n",
        "    nn.Linear(hidden_size, hidden_size),\n",
        "    nn.BatchNorm1d(hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Dropout(p=dropout_p),\n",
        "    nn.Linear(hidden_size, output_size)\n",
        ")\n",
        "'''\n",
        "# model description\n",
        "summary(model,(1,8,8)) # C, H, W\n",
        "\n",
        "# Define loss function and optimizer\n",
        "# Either torch.nn.NLLLoss or torch.nn.CrossEntropyLoss can be used: CrossEntropyLoss (https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html) implements softmax internally\n",
        "loss_fn = nn.CrossEntropyLoss()\n",
        "\n",
        "# Optimizer: optimizer object that will hold the current state and will update the parameters based on the computed gradients\n",
        "# for param in model.parameters(): print(param.data)\n",
        "optimizer = optim.Adam(model.parameters(), lr=learning_rate, weight_decay=regularization_param)\n",
        "\n",
        "# Train the model and predict on test samples to estimate accuracy\n",
        "# history stores losses, accuracy, actual labels and predictions\n",
        "history = train(model, optimizer, loss_fn, num_epochs, train_dl, test_dl)\n",
        "\n",
        "# plot losses along epochs\n",
        "plot_losses(history)\n",
        "# plot confusion matrix\n",
        "plot_accuracy_from_predictions(history)\n",
        "#plot_accuracy(hist)\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "sO8jZzD_Jauh",
        "outputId": "6c5759eb-d14f-4051-9072-9927c130a341",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(1437, 64)\n",
            "Number of examples in training set: torch.Size([1437, 1, 8, 8])\n",
            "Number of examples in test set: torch.Size([360, 1, 8, 8])\n",
            "----------------------------------------------------------------\n",
            "        Layer (type)               Output Shape         Param #\n",
            "================================================================\n",
            "            Conv2d-1              [-1, 8, 8, 8]              80\n",
            "              ReLU-2              [-1, 8, 8, 8]               0\n",
            "         MaxPool2d-3              [-1, 8, 4, 4]               0\n",
            "           Flatten-4                  [-1, 128]               0\n",
            "            Linear-5                    [-1, 8]           1,032\n",
            "       BatchNorm1d-6                    [-1, 8]              16\n",
            "              ReLU-7                    [-1, 8]               0\n",
            "            Linear-8                    [-1, 8]              72\n",
            "       BatchNorm1d-9                    [-1, 8]              16\n",
            "             ReLU-10                    [-1, 8]               0\n",
            "          Dropout-11                    [-1, 8]               0\n",
            "           Linear-12                   [-1, 10]              90\n",
            "================================================================\n",
            "Total params: 1,306\n",
            "Trainable params: 1,306\n",
            "Non-trainable params: 0\n",
            "----------------------------------------------------------------\n",
            "Input size (MB): 0.00\n",
            "Forward/backward pass size (MB): 0.01\n",
            "Params size (MB): 0.00\n",
            "Estimated Total Size (MB): 0.02\n",
            "----------------------------------------------------------------\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy on test set: 0.9217\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### CNN model parameters"
      ],
      "metadata": {
        "id": "1VqJ9dVKS39v"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8NJiUPV47sgv"
      },
      "source": [
        "The number of parameters depend on the kernel size, the number of input channels and the number of output features.\n",
        "\n",
        "In the previous example, the architecture returned by `summary` is:\n",
        "\n",
        "|        Layer (type)       |        Output Shape     |    Param #|\n",
        "| --- | ---: | ---: |\n",
        "|            Conv2d-1       |       [-1, 8, 8, 8]     |         80|\n",
        "|              ReLU-2       |       [-1, 8, 8, 8]     |          0|\n",
        "|         MaxPool2d-3       |       [-1, 8, 4, 4]     |          0|\n",
        "|           Flatten-4       |           [-1, 128]     |          0|\n",
        "|            Linear-5       |             [-1, 8]     |     1,032|\n",
        "| BatchNorm1d-6 |  [-1, 8]        |      16 |\n",
        "|              ReLU-7       |             [-1, 8]     |         0|\n",
        "|            Linear-8       |             [-1, 8]     |         72|\n",
        "| BatchNorm1d-9 |  [-1, 8]        |      16 |\n",
        "|              ReLU-10       |             [-1, 8]     |          0|\n",
        "|           Dropout-11       |             [-1, 8]     |          0|\n",
        "|           Linear-12       |            [-1, 10]     |         90|\n",
        "\n",
        "In the summary above, the output shape format is NCHW and therefore `-1` refers to the batch size which can be replaced by some arbitrary value. The input, before applying the `Conv2d` layer, has C=1 since its a gray image.\n",
        "\n",
        "The summary shows we have 80 parameters for the first convolution, since there are 9 parameters for the 3$\\times$3 kernel plus one additive parameters (bias). In total there are 10 parameters for each convolution map. However, since the depth of the output of the convulational layer is 8, i.e., the model extracts 8 different feature maps, and hence uses 80 parameters for the `Conv2d`layer.\n",
        "\n",
        "`ReLu`, `MaxPool2d` or `Flatten` do not add new parameters. However, `MaxPool2d` reduces the size of each feature map to 4$\\times$4, which means that after flattenning it, there are only 16 values per map to be fed into the fully connected linear layers. For instance, `Linear-5` ingests those 16$\\times$8=128 values and maps them to a 8-node layer. The number of parameters for `Linear-5` is then (128+1)$\\times$8=1032."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Adapt parameters to a different dataset"
      ],
      "metadata": {
        "id": "U6PtuxFvVKKv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The code above shows how to adapt the script that *that implements a convolutional neural network with PyTorch over the mnist 8 by 8 practice data set* to a much larger data set called [CIFAR10](https://www.cs.toronto.edu/~kriz/cifar.html). Each example in `CIFAR10` is a color image of size 32$\\times$32. This means that C=3, H=32 and W=32, while in the previous example with `MNIST`, C=1, H=8 and W=8.\n",
        "\n",
        "At this point we use the same small convolutional neural network as before. The output size, which is the number of classes is still 10 for `CIFAR10`.\n",
        "\n",
        "Firstly, **change your runtime to CPU** (we will see in the following example how to use GPU) and run the *Improved (more modular) script that implements a neural network with PyTorch over the mnist 8 by 8 practice data set* to define the auxiliary functions that this script uses."
      ],
      "metadata": {
        "id": "zv7hxLcaVvvw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script that adapts the CNN designed with PyTorch for MNIST to the CIFAR10 data set\n",
        "\n",
        "'''\n",
        "This code does the following:\n",
        "    Splits the dataset into training and testing sets.\n",
        "    Standardizes the features using StandardScaler.\n",
        "    Reshapes dataset to fit the model\n",
        "    Instantiates the model (NN or CNN)\n",
        "    Defines the loss function (Cross Entropy Loss) and optimizer (Adam).\n",
        "    Trains the model for num_epochs epochs.\n",
        "    Tests the trained model on the test set and evaluates the accuracy.\n",
        "'''\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "from torchsummary import summary\n",
        "from torch.utils.data import DataLoader, TensorDataset\n",
        "import torchvision\n",
        "import torchvision.transforms as transforms\n",
        "from sklearn.datasets import  load_digits\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import ConfusionMatrixDisplay\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "import numpy as np\n",
        "\n",
        "################################################################################ Data and parameters\n",
        "SHOW=True # show some images\n",
        "\n",
        "# parameter constants\n",
        "test_size=0.2\n",
        "hidden_size = 8\n",
        "batch_size= 250\n",
        "num_epochs = 5\n",
        "# Optimizer specific options\n",
        "learning_rate=0.001\n",
        "regularization_param=0.001\n",
        "# Dropout: if p>0\n",
        "dropout_p=0.1 # During training, randomly zeroes some of the elements of the input tensor with probability p.\n",
        "\n",
        "transform = transforms.Compose(\n",
        "    [transforms.ToTensor(),\n",
        "     transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))])\n",
        "\n",
        "# CIFAR10: 60000 32x32 color images in 10 classes, with 6000 images per class\n",
        "train_dataset = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform)\n",
        "\n",
        "test_dataset = torchvision.datasets.CIFAR10(root='./data', train=False, download=True, transform=transform)\n",
        "\n",
        "train_dl = torch.utils.data.DataLoader(train_dataset, batch_size=batch_size,shuffle=True)\n",
        "\n",
        "test_dl = torch.utils.data.DataLoader(test_dataset, batch_size=batch_size,shuffle=False)\n",
        "\n",
        "classes = ('plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck')\n",
        "\n",
        "def imshow(img, labels):\n",
        "        img = img * 0.5 + 0.5  # unnormalize\n",
        "        npimg = img.numpy()\n",
        "        print(npimg.shape)\n",
        "        plt.imshow(np.transpose(npimg, (1, 2, 0)))\n",
        "        plt.title(' '.join('%5s' % classes[labels[j]] for j in range(batch_size)))\n",
        "        plt.show()\n",
        "\n",
        "if SHOW:\n",
        "    # get some random training images\n",
        "    dataiter = iter(train_dl)\n",
        "    images, labels = next(dataiter)\n",
        "    print(images[0].shape) # 3*32*32\n",
        "    print(type(images[0])) # torch tensor\n",
        "    # show images\n",
        "    image_batch=torchvision.utils.make_grid(images)\n",
        "    #print(image_batch[0].shape)\n",
        "    #imshow(image_batch, labels)\n",
        "\n",
        "\n",
        "# Instantiate the model\n",
        "dataiter = iter(train_dl)\n",
        "images, labels = next(dataiter)\n",
        "(C,H,W)=images[0].shape # 3*32*32\n",
        "output_size = len(classes)\n",
        "\n",
        "########################################################################### train and test, pre-processing\n",
        "\n",
        "if SHOW:\n",
        "    class_names = [str(i) for i in range(10)]\n",
        "    # Plot the images\n",
        "    plt.figure(figsize=(10, 5))\n",
        "    image_count = 0\n",
        "    for images, labels in train_dl:\n",
        "        for i in range(len(images)):\n",
        "            plt.subplot(4, 5, image_count + 1)\n",
        "            plt.imshow(np.transpose(images[i], (1, 2, 0)), cmap=\"gray\")\n",
        "            plt.title(class_names[labels[i]])\n",
        "            plt.axis('off')\n",
        "            image_count += 1\n",
        "            if image_count >= 20:\n",
        "                break\n",
        "        if image_count >= 20:\n",
        "            break\n",
        "    plt.show()\n",
        "\n",
        "###################################################################################### CNN  model\n",
        "model=nn.Sequential(\n",
        "    nn.Conv2d(in_channels=C,out_channels=8,kernel_size=3,padding=1),\n",
        "    nn.ReLU(),\n",
        "    nn.MaxPool2d(kernel_size=2),\n",
        "    nn.Flatten(),\n",
        "    nn.Linear(2*W*H, hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(hidden_size, hidden_size),\n",
        "    nn.ReLU(),\n",
        "    nn.Dropout(p=dropout_p),\n",
        "    nn.Linear(hidden_size, output_size)\n",
        ")\n",
        "\n",
        "# to the correct processor:: 'cpu' or 'cuda'\n",
        "#model=model.to('cpu')\n",
        "\n",
        "# model description\n",
        "summary(model,(C,H,W)) # C, H, W\n",
        "\n",
        "# Define loss function and optimizer\n",
        "# Either torch.nn.NLLLoss or torch.nn.CrossEntropyLoss can be used: CrossEntropyLoss (https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html) implements softmax internally\n",
        "loss_fn = nn.CrossEntropyLoss()\n",
        "\n",
        "# Optimizer: optimizer object that will hold the current state and will update the parameters based on the computed gradients\n",
        "# for param in model.parameters(): print(param.data)\n",
        "optimizer = optim.Adam(model.parameters(), lr=learning_rate, weight_decay=regularization_param)\n",
        "\n",
        "# Train the model and predict on test samples to estimate accuracy\n",
        "# history stores losses, accuracy, actual labels and predictions\n",
        "history = train(model, optimizer, loss_fn, num_epochs, train_dl, test_dl)\n",
        "\n",
        "# plot losses along epochs\n",
        "plot_losses(history)\n",
        "# plot confusion matrix\n",
        "plot_accuracy_from_predictions(history)\n",
        "#plot_accuracy(hist)\n"
      ],
      "metadata": {
        "id": "UeGxS8kNVu0A",
        "outputId": "40cc2ec4-9b4f-4ee1-ec3f-b53160ecd87a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Files already downloaded and verified\n",
            "Files already downloaded and verified\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([3, 32, 32])\n",
            "<class 'torch.Tensor'>\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n",
            "WARNING:matplotlib.image:Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 20 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "----------------------------------------------------------------\n",
            "        Layer (type)               Output Shape         Param #\n",
            "================================================================\n",
            "            Conv2d-1            [-1, 8, 32, 32]             224\n",
            "              ReLU-2            [-1, 8, 32, 32]               0\n",
            "         MaxPool2d-3            [-1, 8, 16, 16]               0\n",
            "           Flatten-4                 [-1, 2048]               0\n",
            "            Linear-5                    [-1, 8]          16,392\n",
            "              ReLU-6                    [-1, 8]               0\n",
            "            Linear-7                    [-1, 8]              72\n",
            "              ReLU-8                    [-1, 8]               0\n",
            "           Dropout-9                    [-1, 8]               0\n",
            "           Linear-10                   [-1, 10]              90\n",
            "================================================================\n",
            "Total params: 16,778\n",
            "Trainable params: 16,778\n",
            "Non-trainable params: 0\n",
            "----------------------------------------------------------------\n",
            "Input size (MB): 0.01\n",
            "Forward/backward pass size (MB): 0.16\n",
            "Params size (MB): 0.06\n",
            "Estimated Total Size (MB): 0.23\n",
            "----------------------------------------------------------------\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy on test set: 0.4247\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O1QsEp5T7sgx"
      },
      "source": [
        "### Receptive Fields"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G5xAPJ5_7sgx"
      },
      "source": [
        "The *receptive field* is the area of an image that is involved in the calculation of a layer."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8-m_ec6O7sgy"
      },
      "source": [
        "<img alt=\"Secondary precedents of conv2 layer\" width=\"700\" caption=\"Secondary precedents of Conv2 layer\" id=\"preced2\" src=\"https://github.com/fastai/fastbook/blob/master/images/att_00069.png?raw=1\">"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iSJE4WSl7sgy"
      },
      "source": [
        "In this example, we have just two convolutional layers, each of stride 2, so this is now tracing right back to the input image. We can see that a 7×7 area of cells in the input layer is used to calculate the single green cell in the Conv2 layer. This 7×7 area is the *receptive field* in the input of the green activation in Conv2. We can also see that a second filter kernel is needed now, since we have two layers.\n",
        "\n",
        "As you see from this example, the deeper we are in the network (specifically, the more stride-2 convs we have before a layer), the larger the receptive field for an activation in that layer. A large receptive field means that a large amount of the input image is used to calculate each activation in that layer is. We now know that in the deeper layers of the network we have semantically rich features, corresponding to larger receptive fields. Therefore, we'd expect that we'd need more weights for each of our features to handle this increasing complexity. This is another way of saying the same thing we mentioned in the previous section: when we introduce a stride-2 conv in our network, we should also increase the number of channels."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### CNN as Encoders"
      ],
      "metadata": {
        "id": "uSJ_lA-7OKk6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "[LeNet](http://vision.stanford.edu/cs598_spring07/papers/Lecun98.pdf),  [AlexNet](https://dl.acm.org/doi/10.1145/3065386) and  [VGG Net](https://arxiv.org/abs/1409.1556) are examples of convolutional neural networks for image classification. Typically, they have an input layer which is a tensor that represents an image with dimension *(number rows, number columns, number channels)*, followed by sets of *convolutional* layers, *ReLu* layers, and *pooling* layers, and at the end they have a couple of   *fully connected layers*  followed by a *sofwmax* or a *sigmoid layer*.\n",
        "\n",
        "The idea behind those kind of architectures is to extrat *deep* features through the sequential application of convolutional and maxpool (or stride larger than 1) layers. In that sense, the network is designed to encode deep features of the input into its deep layers.\n",
        "\n",
        "LeNet:\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1-Nxj4sRWiWmjWcPgVnqcoSItiuJo38oH\" width=\"700\" >\n",
        "\n",
        "\n",
        "VGG-net:\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1hoR6Qxda7Ls0VsY-xAzSz1ddlL6IEAnT\" width=\"700\" >\n",
        "\n",
        "\n",
        "\n",
        "Those kind of networks exhibit the following structure:\n",
        "1.  reduction of width and height dimensions of input through each layer in this network;\n",
        "2. accompanied by an organized increment in the number of features (channels) in each layer.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "aSMVUgTnFVz2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Resnets"
      ],
      "metadata": {
        "id": "wXks4Spcd0W7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The early convolutional neural network had a few layers and possibly large kernels (up to 11$\\times$11) for the  [AlexNet](https://dl.acm.org/doi/10.1145/3065386). Later influential models like the [VGG Net](https://arxiv.org/abs/1409.1556) used very small convolution filters and deeper networks which are more powerfull but also are more difficult to train due to the so-called *degradation problem*:  with the network depth increasing, accuracy gets saturated and then degrades rapidly.\n",
        "\n",
        "That problem can be overcome with residual networks known as [resnets](https://arxiv.org/abs/1512.03385). The main idea is that it is easier to train neural network to find a vanishing mapping than to approximate more complicated functions. The residual block (shown below) converts the problem of training $F(x)$ for an arbitrary expected output $H(x)$ into the problem of training $F(x)$ for $H(x)-x$, which is a residual and should ideally vanish.\n",
        "\n",
        "<img src=\"https://miro.medium.com/v2/resize:fit:1140/format:webp/1*D0F3UitQ2l5Q0Ak-tjEdJg.png\" width=\"400\" >\n",
        "\n",
        "\n",
        "As an exemple, see below the full diagram that describes `resnet18`. The arrows represent the application of the identity function. That architecture, proposed in https://arxiv.org/abs/1512.03385, reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. Those residual networks are easier to optimize, and can gain accuracy from considerably increased depth.\n",
        "\n",
        "<img src=\"https://www.researchgate.net/profile/Sajid-Iqbal-13/publication/336642248/figure/fig1/AS:839151377203201@1577080687133/Original-ResNet-18-Architecture_W640.jpg\" width=\"700\" >"
      ],
      "metadata": {
        "id": "ggmRGNdnhZI8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Image segmentation"
      ],
      "metadata": {
        "id": "oa7bw6mYcSIN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Image segmentation (see for instance https://www.ibm.com/topics/image-segmentation) is a computer vision technique that partitions a digital image into discrete groups of pixels called image segments.\n",
        "\n",
        "Unlike image classification, where the entire image is one example to be labeled, image segmentation processes visual data at the pixel level, using various techniques to annotate individual pixels as belonging to a specific class or instance.\n",
        "\n",
        "Traditional image segmentation techniques use information from a pixel's color values and related characteristics like brightness, contrast or intensity  for feature extraction. Neural networks of deep learning image segmentation models are trained on annotated dataset of images and tend to require much more computational resourses. Despite those tradeoffs in computing requirements and training time, deep learning models consistently outperform traditional models and form the basis of most ongoing advancements in computer vision.\n",
        "\n",
        "According to https://www.ibm.com/topics/image-segmentation, prominent deep learning models used in image segmentation include:\n",
        "\n",
        "1. Fully Convolutional Networks (FCNs): FCNs, often used for semantic segmentation, are a type of convolutional neural network (CNN) with no fixed layers. An encoder network passes visual input data through convolutional layers to extract features relevant to segmentation or classification, and compresses (or downsamples) this feature data to remove non-essential information. This compressed data is then fed into decoder layers, upsampling the extracted feature data to reconstruct the input image with segmentation masks.\n",
        "\n",
        "2. U-Nets: U-Nets modify FCN architecture to reduce data loss during downsampling with skip connections, preserving greater detail by selectively bypassing some convolutional layers as information and gradients move through the neural network. Its name is derived from the shape of diagrams demonstrating the arrangement of its layers.\n",
        "\n",
        "3. Deeplab: Like U-Nets, Deeplab is a modified FCN architecture. In addition to skip connections, it uses diluted (or “atrous”) convolution to yield larger output maps without necessitating additional computational power.\n",
        "\n",
        "4. Mask R-CNNs: Mask R-CNNs are a leading model for instance segmentation. Mask R-CNNs combine a region proposal network (RPN) that generates bounding boxes for each potential instance with an FCN-based “mask head” that generates segmentation masks within each confirmed bounding box.\n",
        "\n",
        "5. Transformers: inspired by the success of transformer models in natural language processing, new models like Vision Transformer (ViT) using attention mechanisms in place of convolutional layers have matched or exceeded CNN performance for computer vision tasks.\n",
        "\n",
        "Below, the architecture of U-nets (https://arxiv.org/abs/1505.04597) is illustrated. The U shape of the diagram represntes the encoder part, that converts input into a small and deep feature map, followed by a decoder part that generates a output with the same number of rows and columns as the input. The output's pixels are labeled such that the it provides a segmentation of the input image.\n",
        "\n",
        "\n",
        "<img src=\"https://www.frontiersin.org/files/Articles/841297/fnagi-14-841297-HTML-r2/image_m/fnagi-14-841297-g001.jpg\" width=\"700\" >\n",
        "\n",
        "This approach for image segmentation can be applied to large images by an *overlap-tile strategy* as illustrated by Figure 2 in https://arxiv.org/abs/1505.04597.\n",
        "\n",
        "A commented example of the use of a U-Net to segment street photos for  self-driving cars is available at [Image_Segmentation_with_Unet.ipynb](Image_Segmentation_with_Unet.ipynb). This is implemented with the `fastai` package.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "UhlpjU4PkXF0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Pre-trained models and transfer learning"
      ],
      "metadata": {
        "id": "9zSYuXnzG8Wz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "One of the main tools available im Machine Learning is called *Transfer learning* which allows us to leverage powerful resources that are already available. Currently, there are many pre-trained models freely available, which have been trained with large amounts of data. We can access those pre-trained models to solve the problem at hand. In order to do that, we need:\n",
        "1. To adapt the input size;\n"
      ],
      "metadata": {
        "id": "al2DaEjZCDff"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title PyTorch script that uploads a pre-trained Resnet for the Cifar10 data set\n",
        "# code adapted from https://github.com/rasbt/machine-learning-book/blob/main/ch14/ch14_part1.py\n",
        "\n",
        "\n",
        "# todo -- just with PyTorch\n",
        "# 1. Read CIFAR10\n",
        "# 2. Upload pre-trained resnet\n",
        "# 3. Customize model to the data\n",
        "# 4. Fine tune\n",
        "# 5. Save tuned model\n",
        "# 6. predict with savel model\n",
        "\n",
        "'''\n",
        "This code does the following:\n",
        "    Splits the dataset into training and testing sets.\n",
        "    Standardizes the features using StandardScaler.\n",
        "    Reshapes dataset to fit the model\n",
        "    Instantiates the model (CNN)\n",
        "    Defines the loss function (Cross Entropy Loss) and optimizer (Adam).\n",
        "    Trains the model for num_epochs epochs.\n",
        "    Tests the trained model on the test set and evaluates the accuracy.\n",
        "'''\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "from torchsummary import summary\n",
        "from torch.utils.data import DataLoader, TensorDataset\n",
        "import torchvision\n",
        "import torchvision.transforms as transforms\n",
        "from torchvision.models import resnet18, ResNet18_Weights\n",
        "from sklearn.datasets import  load_digits\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import ConfusionMatrixDisplay\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "import numpy as np\n",
        "from pathlib import Path\n",
        "from tqdm import tqdm\n",
        "\n",
        "################################################################################  functions\n",
        "\n",
        "def train(model, optimizer, loss_fn, num_epochs, train_dl, valid_dl):\n",
        "    '''\n",
        "    Main function to train and test the model\n",
        "    '''\n",
        "    # lists to strore losses and accuracies\n",
        "    loss_hist_train = [0] * num_epochs\n",
        "    accuracy_hist_train = [0] * num_epochs\n",
        "    loss_hist_valid = [0] * num_epochs\n",
        "    accuracy_hist_valid = [0] * num_epochs\n",
        "    # main loop through epochs\n",
        "    for epoch in range(num_epochs):\n",
        "        # training mode\n",
        "        model.train()\n",
        "        for x_batch, y_batch in tqdm(train_dl):\n",
        "            x_batch,y_batch=x_batch.to(device),y_batch.to(device)  # edited\n",
        "            # core of the learning process: predict and fit\n",
        "            pred = model(x_batch)\n",
        "            loss = loss_fn(pred, y_batch)\n",
        "            loss.backward()\n",
        "            optimizer.step()\n",
        "            optimizer.zero_grad()\n",
        "            # compute train loss and accuracy\n",
        "            loss_hist_train[epoch] += loss.item()*y_batch.size(0)\n",
        "            is_correct = (torch.argmax(pred, dim=1) == y_batch).float()\n",
        "            accuracy_hist_train[epoch] += is_correct.sum()\n",
        "        # compute average loss per epoch\n",
        "        loss_hist_train[epoch] /= len(train_dl.dataset)\n",
        "        accuracy_hist_train[epoch] /= len(train_dl.dataset)\n",
        "        # we also put the model in evaluation mode, so that specific layers such as dropout or batch normalization layers behave correctly.\n",
        "        model.eval()\n",
        "        with torch.no_grad():\n",
        "            for x_batch, y_batch in valid_dl:\n",
        "                x_batch,y_batch=x_batch.to(device),y_batch.to(device) # edited\n",
        "                # predict\n",
        "                pred = model(x_batch)\n",
        "                loss = loss_fn(pred, y_batch)\n",
        "                loss_hist_valid[epoch] += loss.item()*y_batch.size(0)\n",
        "                is_correct = (torch.argmax(pred, dim=1) == y_batch).float()\n",
        "                accuracy_hist_valid[epoch] += is_correct.sum()\n",
        "                if epoch==0:\n",
        "                    preds,actuals=torch.argmax(pred, dim=1),y_batch\n",
        "                else:\n",
        "                    preds=torch.cat((preds,torch.argmax(pred, dim=1)),dim=0)\n",
        "                    actuals=torch.cat((actuals,y_batch),dim=0)\n",
        "        # compute average loss per epoch\n",
        "        loss_hist_valid[epoch] /= len(valid_dl.dataset)\n",
        "        accuracy_hist_valid[epoch] /= len(valid_dl.dataset)\n",
        "        # print accuracy\n",
        "        if (epoch+1) % 100==0:\n",
        "            print(f'Epoch {epoch+1} accuracy: {accuracy_hist_train[epoch]:.4f} val_accuracy: {accuracy_hist_valid[epoch]:.4f}')\n",
        "    return loss_hist_train, loss_hist_valid, accuracy_hist_train, accuracy_hist_valid, preds,actuals\n",
        "\n",
        "\n",
        "def plot_accuracy_from_predictions(hist):\n",
        "    ''' Creates and prints confusion matrix from a model and a set of examples\n",
        "    Inputs\n",
        "    ------\n",
        "    hist: tuple\n",
        "        where hist[4] is the list of predicted values for test and hist[5] are the actual labels\n",
        "    '''\n",
        "    pred=[t.item() for t in hist[4]]\n",
        "    actual=[t.item() for t in hist[5]]\n",
        "    labels = np.unique(actual)\n",
        "    disp = ConfusionMatrixDisplay.from_predictions(actual,pred,labels=labels)\n",
        "    # print global accuracy\n",
        "    accuracy=np.sum(np.diagonal(disp.confusion_matrix))/np.sum(disp.confusion_matrix)\n",
        "    print(f'Accuracy on test set: {accuracy:.4f}')\n",
        "    plt.show()\n",
        "\n",
        "# TypeError: can't convert cuda:0 device type tensor to numpy. Use Tensor.cpu() to copy the tensor to host memory first.\n",
        "def plot_losses(hist):\n",
        "    ''' plots train and test loss\n",
        "    Input\n",
        "    ------\n",
        "    history, the output of function train()\n",
        "    '''\n",
        "    x_arr = np.arange(len(hist[0])) + 1\n",
        "    fig = plt.figure(figsize=(12, 4))\n",
        "    ax = fig.add_subplot(1, 2, 1)\n",
        "    ax.plot(x_arr, hist[0] , '-o', label='Train loss')\n",
        "    ax.plot(x_arr, hist[1], '--<', label='Test loss')\n",
        "    ax.set_xlabel('Epoch', size=15)\n",
        "    ax.set_ylabel('Loss', size=15)\n",
        "    ax.legend(fontsize=15)\n",
        "    ax = fig.add_subplot(1, 2, 2)\n",
        "    ax.plot(x_arr, [t.item() for t in hist[2]], '-o', label='Train acc.') # tensors in cuda cannot be plotted; .item extracts the value to cpu\n",
        "    ax.plot(x_arr, [t.item() for t in hist[3]], '--<', label='Test acc.')\n",
        "    ax.legend(fontsize=15)\n",
        "    ax.set_xlabel('Epoch', size=15)\n",
        "    ax.set_ylabel('Accuracy', size=15)\n",
        "    plt.show()\n",
        "\n",
        "################################################################################ Data and parameters\n",
        "SHOW=False # show some images\n",
        "DOWNLOAD=True\n",
        "\n",
        "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')  # checks is cuda (GPU) is available\n",
        "print('device',device)\n",
        "\n",
        "# parameter constants\n",
        "test_size=0.2\n",
        "hidden_size = 8\n",
        "batch_size= 500\n",
        "num_epochs = 3\n",
        "# CIFAR-10 images\n",
        "NUM_CLASSES=10\n",
        "# Optimizer specific options\n",
        "learning_rate=0.001\n",
        "regularization_param=0.001\n",
        "# Dropout: if p>0\n",
        "dropout_p=0.1 # During training, randomly zeroes some of the elements of the input tensor with probability p.\n",
        "\n",
        "# Data augmentation and normalization for training\n",
        "# https://pytorch.org/vision/main/auto_examples/transforms/plot_transforms_illustrations.html#sphx-glr-auto-examples-transforms-plot-transforms-illustrations-py\n",
        "# Just normalization for validation\n",
        "data_transforms = {\n",
        "    'train': transforms.Compose([\n",
        "        transforms.RandomResizedCrop(224), # see \"Size matters\" https://arxiv.org/pdf/2102.01582.pdf\n",
        "        transforms.RandomHorizontalFlip(),  #optional\n",
        "        transforms.ToTensor(),\n",
        "        transforms.Normalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225])\n",
        "    ]),\n",
        "    'test': transforms.Compose([\n",
        "        transforms.Resize(256), # bilinear by default\n",
        "        transforms.CenterCrop(224),\n",
        "        transforms.ToTensor(),\n",
        "        transforms.Normalize([0.485, 0.456, 0.406], [0.229, 0.224, 0.225])\n",
        "    ]),\n",
        "}\n",
        "\n",
        "\n",
        "# Create directory to store images\n",
        "path=Path('./gdrive/MyDrive/PML_2024/cifar10')\n",
        "if not path.exists():\n",
        "    path.mkdir(exist_ok=True, parents=True)\n",
        "\n",
        "# read CIFAR10: 60000 32x32 color images in 10 classes, with 6000 images per class\n",
        "train_dataset = torchvision.datasets.CIFAR10(root=path, train=True,download=DOWNLOAD, transform=data_transforms['train'])\n",
        "test_dataset = torchvision.datasets.CIFAR10(root=path, train=False,download=DOWNLOAD, transform=data_transforms['test'])\n",
        "#after transform\n",
        "C=3\n",
        "H=224\n",
        "W=224\n",
        "\n",
        "# CIFAR10 classes\n",
        "class_names = ('plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck')\n",
        "\n",
        "train_dl = DataLoader(train_dataset, batch_size=batch_size,shuffle=True)\n",
        "test_dl = DataLoader(test_dataset, batch_size=batch_size,shuffle=False)\n",
        "\n",
        "def imshow(inp, title=None):\n",
        "    \"\"\"Display image for Tensor.\"\"\"\n",
        "    inp = inp.numpy().transpose((1, 2, 0))\n",
        "    mean = np.array([0.485, 0.456, 0.406])\n",
        "    std = np.array([0.229, 0.224, 0.225])\n",
        "    inp = std * inp + mean\n",
        "    inp = np.clip(inp, 0, 1)\n",
        "    plt.imshow(inp)\n",
        "    if title is not None:\n",
        "        plt.title(title)\n",
        "    plt.pause(0.001)  # pause a bit so that plots are updated\n",
        "\n",
        "if SHOW:\n",
        "    # Get a batch of training data\n",
        "    inputs, classes = next(iter(train_dl))\n",
        "    # Make a grid from batch\n",
        "    out = torchvision.utils.make_grid(inputs)\n",
        "    imshow(out, title=[class_names[x] for x in classes])\n",
        "    plt.show()\n",
        "\n",
        "###################################################################################### upload resnet model\n",
        "\n",
        "\n",
        "model = resnet18(pretrained=True)\n",
        "model.fc=nn.Linear(512, NUM_CLASSES)\n",
        "\n",
        "model.requires_grad_(False)\n",
        "model.fc.requires_grad_(True)\n",
        "\n",
        "# to the correct processor\n",
        "model=model.to(device)\n",
        "\n",
        "# model description\n",
        "summary(model,(C,H,W)) # C, H, W\n",
        "\n",
        "# Define loss function and optimizer\n",
        "# Either torch.nn.NLLLoss or torch.nn.CrossEntropyLoss can be used: CrossEntropyLoss (https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html) implements softmax internally\n",
        "loss_fn = nn.CrossEntropyLoss()\n",
        "\n",
        "# Optimizer: optimizer object that will hold the current state and will update the parameters based on the computed gradients\n",
        "# for param in model.parameters(): print(param.data)\n",
        "optimizer = optim.Adam(model.parameters(), lr=learning_rate, weight_decay=regularization_param)\n",
        "\n",
        "# Train the model and predict on test samples to estimate accuracy\n",
        "# history stores losses, accuracy, actual labels and predictions\n",
        "history = train(model, optimizer, loss_fn, num_epochs, train_dl, test_dl)\n",
        "\n",
        "# plot losses along epochs\n",
        "plot_losses(history)\n",
        "# plot confusion matrix\n",
        "plot_accuracy_from_predictions(history)\n",
        "#plot_accuracy(hist)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "8_I3mBtISxI4",
        "outputId": "ab0e5ffd-8701-4a60-d1ba-49856ac5c8ad"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "device cuda\n",
            "Files already downloaded and verified\n",
            "Files already downloaded and verified\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/torchvision/models/_utils.py:208: UserWarning: The parameter 'pretrained' is deprecated since 0.13 and may be removed in the future, please use 'weights' instead.\n",
            "  warnings.warn(\n",
            "/usr/local/lib/python3.10/dist-packages/torchvision/models/_utils.py:223: UserWarning: Arguments other than a weight enum or `None` for 'weights' are deprecated since 0.13 and may be removed in the future. The current behavior is equivalent to passing `weights=ResNet18_Weights.IMAGENET1K_V1`. You can also use `weights=ResNet18_Weights.DEFAULT` to get the most up-to-date weights.\n",
            "  warnings.warn(msg)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "----------------------------------------------------------------\n",
            "        Layer (type)               Output Shape         Param #\n",
            "================================================================\n",
            "            Conv2d-1         [-1, 64, 112, 112]           9,408\n",
            "       BatchNorm2d-2         [-1, 64, 112, 112]             128\n",
            "              ReLU-3         [-1, 64, 112, 112]               0\n",
            "         MaxPool2d-4           [-1, 64, 56, 56]               0\n",
            "            Conv2d-5           [-1, 64, 56, 56]          36,864\n",
            "       BatchNorm2d-6           [-1, 64, 56, 56]             128\n",
            "              ReLU-7           [-1, 64, 56, 56]               0\n",
            "            Conv2d-8           [-1, 64, 56, 56]          36,864\n",
            "       BatchNorm2d-9           [-1, 64, 56, 56]             128\n",
            "             ReLU-10           [-1, 64, 56, 56]               0\n",
            "       BasicBlock-11           [-1, 64, 56, 56]               0\n",
            "           Conv2d-12           [-1, 64, 56, 56]          36,864\n",
            "      BatchNorm2d-13           [-1, 64, 56, 56]             128\n",
            "             ReLU-14           [-1, 64, 56, 56]               0\n",
            "           Conv2d-15           [-1, 64, 56, 56]          36,864\n",
            "      BatchNorm2d-16           [-1, 64, 56, 56]             128\n",
            "             ReLU-17           [-1, 64, 56, 56]               0\n",
            "       BasicBlock-18           [-1, 64, 56, 56]               0\n",
            "           Conv2d-19          [-1, 128, 28, 28]          73,728\n",
            "      BatchNorm2d-20          [-1, 128, 28, 28]             256\n",
            "             ReLU-21          [-1, 128, 28, 28]               0\n",
            "           Conv2d-22          [-1, 128, 28, 28]         147,456\n",
            "      BatchNorm2d-23          [-1, 128, 28, 28]             256\n",
            "           Conv2d-24          [-1, 128, 28, 28]           8,192\n",
            "      BatchNorm2d-25          [-1, 128, 28, 28]             256\n",
            "             ReLU-26          [-1, 128, 28, 28]               0\n",
            "       BasicBlock-27          [-1, 128, 28, 28]               0\n",
            "           Conv2d-28          [-1, 128, 28, 28]         147,456\n",
            "      BatchNorm2d-29          [-1, 128, 28, 28]             256\n",
            "             ReLU-30          [-1, 128, 28, 28]               0\n",
            "           Conv2d-31          [-1, 128, 28, 28]         147,456\n",
            "      BatchNorm2d-32          [-1, 128, 28, 28]             256\n",
            "             ReLU-33          [-1, 128, 28, 28]               0\n",
            "       BasicBlock-34          [-1, 128, 28, 28]               0\n",
            "           Conv2d-35          [-1, 256, 14, 14]         294,912\n",
            "      BatchNorm2d-36          [-1, 256, 14, 14]             512\n",
            "             ReLU-37          [-1, 256, 14, 14]               0\n",
            "           Conv2d-38          [-1, 256, 14, 14]         589,824\n",
            "      BatchNorm2d-39          [-1, 256, 14, 14]             512\n",
            "           Conv2d-40          [-1, 256, 14, 14]          32,768\n",
            "      BatchNorm2d-41          [-1, 256, 14, 14]             512\n",
            "             ReLU-42          [-1, 256, 14, 14]               0\n",
            "       BasicBlock-43          [-1, 256, 14, 14]               0\n",
            "           Conv2d-44          [-1, 256, 14, 14]         589,824\n",
            "      BatchNorm2d-45          [-1, 256, 14, 14]             512\n",
            "             ReLU-46          [-1, 256, 14, 14]               0\n",
            "           Conv2d-47          [-1, 256, 14, 14]         589,824\n",
            "      BatchNorm2d-48          [-1, 256, 14, 14]             512\n",
            "             ReLU-49          [-1, 256, 14, 14]               0\n",
            "       BasicBlock-50          [-1, 256, 14, 14]               0\n",
            "           Conv2d-51            [-1, 512, 7, 7]       1,179,648\n",
            "      BatchNorm2d-52            [-1, 512, 7, 7]           1,024\n",
            "             ReLU-53            [-1, 512, 7, 7]               0\n",
            "           Conv2d-54            [-1, 512, 7, 7]       2,359,296\n",
            "      BatchNorm2d-55            [-1, 512, 7, 7]           1,024\n",
            "           Conv2d-56            [-1, 512, 7, 7]         131,072\n",
            "      BatchNorm2d-57            [-1, 512, 7, 7]           1,024\n",
            "             ReLU-58            [-1, 512, 7, 7]               0\n",
            "       BasicBlock-59            [-1, 512, 7, 7]               0\n",
            "           Conv2d-60            [-1, 512, 7, 7]       2,359,296\n",
            "      BatchNorm2d-61            [-1, 512, 7, 7]           1,024\n",
            "             ReLU-62            [-1, 512, 7, 7]               0\n",
            "           Conv2d-63            [-1, 512, 7, 7]       2,359,296\n",
            "      BatchNorm2d-64            [-1, 512, 7, 7]           1,024\n",
            "             ReLU-65            [-1, 512, 7, 7]               0\n",
            "       BasicBlock-66            [-1, 512, 7, 7]               0\n",
            "AdaptiveAvgPool2d-67            [-1, 512, 1, 1]               0\n",
            "           Linear-68                   [-1, 10]           5,130\n",
            "================================================================\n",
            "Total params: 11,181,642\n",
            "Trainable params: 5,130\n",
            "Non-trainable params: 11,176,512\n",
            "----------------------------------------------------------------\n",
            "Input size (MB): 0.57\n",
            "Forward/backward pass size (MB): 62.79\n",
            "Params size (MB): 42.65\n",
            "Estimated Total Size (MB): 106.01\n",
            "----------------------------------------------------------------\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 100/100 [01:36<00:00,  1.04it/s]\n",
            "100%|██████████| 100/100 [01:35<00:00,  1.04it/s]\n",
            "100%|██████████| 100/100 [01:35<00:00,  1.04it/s]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy on test set: 0.7216\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Deploying ML models in production"
      ],
      "metadata": {
        "id": "d-p_-022euQp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "<img src=\"https://dezyre.gumlet.io/images/blog/machine-learning-model-deployment/Machine_Learning_Model_Deployment_Tutorial.png?w=1100&dpr=1.5\" width=\"700\" >\n",
        "\n",
        "Some useful links:\n",
        "\n",
        "1. Saving and loading `PyTorch`models:  https://pytorch.org/tutorials/beginner/saving_loading_models.html\n",
        "\n",
        "\n",
        "2. Steps to create a web application with `Gradio` to deploy a `PyTorch` model for image classification: https://www.gradio.app/guides/image-classification-in-pytorch\n",
        "\n",
        "3. Gradio + HuggingFace Spaces: A Tutorial: https://www.tanishq.ai/blog/posts/2021-11-16-gradio-huggingface.html"
      ],
      "metadata": {
        "id": "a6I_JCD7fEBL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Script for deploying the corn disease classifier with Gradio\n",
        "\n",
        "import gradio as gr\n",
        "import torch\n",
        "from torchvision import transforms\n",
        "from torchvision.models import resnet18, ResNet18_Weights\n",
        "from torch import nn\n",
        "from PIL import Image # pip install pillow\n",
        "\n",
        "labels = ['Blight','Common_Rust','Gray_Leaf_Spot','Healthy']\n",
        "\n",
        "# Same data transformation that was used for inputs (except data augmentation)\n",
        "data_transform = transforms.Compose([\n",
        "    transforms.Resize(size=(256, 256)),\n",
        "    transforms.ToTensor(),\n",
        "    transforms.Normalize(mean=[0.485, 0.456, 0.406],\n",
        "                        std=[0.229, 0.224, 0.225])\n",
        "])\n",
        "\n",
        "# https://pytorch.org/tutorials/beginner/saving_loading_models.html\n",
        "# Loading Model for Inference with state_dict (recommended)\n",
        "model = resnet18(weights=ResNet18_Weights.DEFAULT)\n",
        "model.fc = nn.Linear(in_features=512, out_features=len(labels))\n",
        "model.load_state_dict(torch.load(\"model.pth\",map_location=torch.device('cpu')))\n",
        "model.eval()\n",
        "\n",
        "def predict(img):\n",
        "    X = data_transform(img).unsqueeze(0) # returns tensor\n",
        "    with torch.no_grad():\n",
        "            predictions = model(X).flatten()\n",
        "            predictions = torch.nn.functional.softmax(predictions)\n",
        "            confidences = {labels[i]: float(predictions[i]) for i in range(len(labels))}\n",
        "    return confidences\n",
        "\n",
        "demo=gr.Interface(fn=predict,\n",
        "             inputs=gr.Image(type=\"pil\"),\n",
        "             outputs=gr.Label(num_top_classes=len(labels)),\n",
        "             examples=[\"Corn_Blight.jpg\", \"Corn_Common_Rust.jpg\",\"Corn_Gray_Spot.jpg\",\"Corn_Health.jpg\"])\n",
        "\n",
        "demo.launch('share=True')"
      ],
      "metadata": {
        "id": "yZXu6FCXetqq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following figure shows the list of files that were created/uploaded to the Hugging Face space in order to create the app available at\n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=1--lEvbmxYxZN8kWsaBc6nNbdi-jLvYoD\" width=\"600\" >\n",
        "\n"
      ],
      "metadata": {
        "id": "YnqQf9MgcG6G"
      }
    }
  ]
}