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TP-ML/solutions/Lab9_solutions.ipynb
2022-06-05 15:43:42 +02:00

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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Lab9_solutions",
"provenance": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"source": [
"In this lab, we'll experiment a bit more with the task of binary classification. We'll be considering four different classifiers, respectively the Logistic Regression, the Linear Discriminant Analysis (LDA), the Quadratic Discriminant Analysis (QDA), and Naïve Bayes. \n",
"\n",
"We'll be using the 'wine.csv' dataset, which contains several attributes of white wines, and each observation is associated to a binary quality value, indicating whethter the wine is of superior quality or not. The present goal is to use the above classifiers to determine the quality group of a wine based on its set of attributes. \n",
"\n",
"The columns of the dataframe contain the following information :\n",
"* fixed_acidity : amount of tartaric acid in g/dm^3\n",
"* volatile_acidity : amount of acetic acid in g/dm^3 \n",
"* citric_acid : amount of citric acid in g/dm^3\n",
"* residual_sugar : amount of remaining sugar after fermentation stops in g/l\n",
"* chlorides : amount of salt in wine \n",
"* free_sulfur_dioxide : amount of free SO2\n",
"* total_sulfur_dioxide : amount of free and bound forms of SO2\n",
"* density : density of the wine\n",
"* pH : PH level of the wine on a scale from 0 to 14\n",
"* sulphates : amount of sulphates \n",
"* alcohol : the percent of alcohol content\n",
"* quality : quality of the wine (1 : superior, 0 : inferior)"
],
"metadata": {
"id": "9qc8zzFDR5Vu",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**Import necessary libraries**"
],
"metadata": {
"id": "OL2bnL0KU_Vg",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "AtfNUtAHZEVv",
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [],
"source": [
"import numpy as np \n",
"import pandas as pd \n",
"from sklearn.metrics import accuracy_score, confusion_matrix, ConfusionMatrixDisplay, roc_curve, roc_auc_score\n",
"from sklearn.model_selection import train_test_split, cross_validate\n",
"from sklearn.linear_model import LogisticRegression\n",
"from sklearn.preprocessing import StandardScaler, RobustScaler\n",
"from sklearn.neighbors import KNeighborsClassifier\n",
"from sklearn.compose import ColumnTransformer\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import norm \n",
"from sklearn.discriminant_analysis import LinearDiscriminantAnalysis, QuadraticDiscriminantAnalysis\n",
"from sklearn.naive_bayes import GaussianNB\n",
"import math\n",
"import seaborn as sns\n",
"import statsmodels.api as sm\n",
"from patsy import dmatrices\n"
]
},
{
"cell_type": "markdown",
"source": [
"# Data exploration"
],
"metadata": {
"id": "yNiuBYj4XFa0",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**1) Read the dataset 'wine.csv', check its properties. Check and handle possible missing values.** "
],
"metadata": {
"id": "kJLA1I0qVCwU",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"file = 'wine.csv'\n",
"df = pd.read_csv(file, index_col=0)\n",
"print(df.info())\n",
"print(df.head())\n",
"print(df.isna().sum())\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "zKQyTrqKZLmg",
"outputId": "d3661716-6332-41f2-f276-78ada9dee2e7",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"Int64Index: 4898 entries, 0 to 4897\n",
"Data columns (total 12 columns):\n",
" # Column Non-Null Count Dtype \n",
"--- ------ -------------- ----- \n",
" 0 fixed_acidity 4898 non-null float64\n",
" 1 volatile_acidity 4898 non-null float64\n",
" 2 citric_acid 4898 non-null float64\n",
" 3 residual_sugar 4898 non-null float64\n",
" 4 chlorides 4898 non-null float64\n",
" 5 free_sulfur_dioxide 4898 non-null float64\n",
" 6 total_sulfur_dioxide 4898 non-null float64\n",
" 7 density 4898 non-null float64\n",
" 8 pH 4898 non-null float64\n",
" 9 sulphates 4898 non-null float64\n",
" 10 alcohol 4898 non-null float64\n",
" 11 quality 4898 non-null int64 \n",
"dtypes: float64(11), int64(1)\n",
"memory usage: 497.5 KB\n",
"None\n",
" fixed_acidity volatile_acidity citric_acid residual_sugar chlorides \\\n",
"0 7.0 0.27 0.36 20.7 0.045 \n",
"1 6.3 0.30 0.34 1.6 0.049 \n",
"2 8.1 0.28 0.40 6.9 0.050 \n",
"3 7.2 0.23 0.32 8.5 0.058 \n",
"4 7.2 0.23 0.32 8.5 0.058 \n",
"\n",
" free_sulfur_dioxide total_sulfur_dioxide density pH sulphates \\\n",
"0 45.0 170.0 1.0010 3.00 0.45 \n",
"1 14.0 132.0 0.9940 3.30 0.49 \n",
"2 30.0 97.0 0.9951 3.26 0.44 \n",
"3 47.0 186.0 0.9956 3.19 0.40 \n",
"4 47.0 186.0 0.9956 3.19 0.40 \n",
"\n",
" alcohol quality \n",
"0 8.8 0 \n",
"1 9.5 0 \n",
"2 10.1 0 \n",
"3 9.9 0 \n",
"4 9.9 0 \n",
"fixed_acidity 0\n",
"volatile_acidity 0\n",
"citric_acid 0\n",
"residual_sugar 0\n",
"chlorides 0\n",
"free_sulfur_dioxide 0\n",
"total_sulfur_dioxide 0\n",
"density 0\n",
"pH 0\n",
"sulphates 0\n",
"alcohol 0\n",
"quality 0\n",
"dtype: int64\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"**2) Look at the distribution of the target variable 'quality' (using a barplot).**\n",
"\n",
"**Do you notice anything ?**"
],
"metadata": {
"id": "DPl9I2xuVSOL",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"categories = df['quality'].value_counts().index.astype(str)\n",
"counts = df['quality'].value_counts().values \n",
"counts = [elem/df.shape[0] for elem in counts]\n",
"print(counts)\n",
"ax.bar(categories, counts, width=0.5)\n",
"ax.set_xlabel(\"Quality\")\n",
"ax.set_title('Distribution of \"Quality\"')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 330
},
"id": "oYULnCz6ZVmu",
"outputId": "d8f63488-0439-4bfe-f826-2b9695f9210f",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0.7835851367905268, 0.21641486320947326]\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Distribution of \"Quality\"')"
]
},
"metadata": {},
"execution_count": 35
},
{
"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": [
"There's a high class imbalance, with around 78% of observations belonging to the class '0'."
],
"metadata": {
"id": "r6-SO9iF7dbb",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**3) Plot a boxplot for each of the predictor variables, while separating for the quality level. Use the 'boxplot' method of the seaborn library.**\n",
"\n",
"**From the obtained boxplots, can you spot the 3 predictors that might seem to be most useful in predicting the target variable 'quality' ?**"
],
"metadata": {
"id": "JWrU6ky2VllI",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"X = df.drop('quality', axis=1)\n",
"for key in X.columns:\n",
" sns.boxplot(x='quality', y=key, data=df)\n",
" plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "OM_sE_Pxj64S",
"outputId": "71b6abca-8e71-47ff-f1c3-af8f842b9715",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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7+uqrEyfBDs9u4kNekvTilspK9JGzhhInSe/ZTY2aV+D+syl/YKriN49dXqvew3fGsfw7madiXxvJyt/2GyVdJ+lkSSHpUxFxf6o8QCr8VroLv5XWT8qZ/9WSeiPiI7YPlDQrYRYAyEqS8rf9BkmnS/qkJEXEa5JeS5EFAHKU6jz/4yRtlHSD7YdtX2f74NFPsr3Ydr/t/o0bN9Y/JQBMU6nKv0nSaZKujYi3Stos6bOjnxQRqyKiIyI6Wlpa6p0RAKatVOX/nKTnIuJH1fF3VfnLAABQB0nKPyJekPQz2ydWN71P0n+nyAIAOUp5ts8SSTdVz/R5WtIFCbMAQFaSlX9EPCKpI9XxASBnXNUTADJE+QNAhih/AMgQ5Q8AGaL8ASBDlD8AZIjyB4AMUf4AkCHKHwAyRPkDQIYofwDIEOUPABmi/AEgQ5Q/AGSI8geADFH+AJAhyh8AMkT5Z2jbtm0qlUoaHBxMHQVAIo6I1Blq0tHREf39/alj7JOVK1eqVCqljqHHH39c5XJZzc3NmjNnTrIc7e3tWrJkSbLjY5ep8trckaG9vT1pjun02rS9NiJed8tcZv6Z2bZtm8rlsiRpcHBQ27ZtS5wI2GXmzJmaOXNm6hhZSHYD9xxNhZnEVVddpSeeeEIRIduaN2+eLr744tSxkNhUeG2ivpj5Z6avr087lvoiQnfeeWfiRMAupVJJCxcunBJLUNMd5Z+ZI488ctwxkNKKFSu0efNmrVixInWUaY/yz8wLL7ww7hhIpVQqaWBgQJI0MDDA7L9glH9mjjrqqHHHQCqjZ/vM/otF+WfmxRdfHHcMpLJj1r+7MSYX5Z+Z008/fdwxkMoxxxwz7hiTi/LPzP7yoT7k5/jjjx8xPuGEExIlyQPln5n77rtvxPjee+9NlAQY6cEHHxwxfuCBBxIlyUPS8rfdaPth27enzJGTzs5ONTY2SpIaGxu1YMGCxImAis7OTjU0VCqpoaGB12bBUs/8l0l6InGGrHR3d+8s/6amJi1atChxIqCC12Z9JSt/23MkLZR0XaoMOWpublZXV5dsq6urS83NzakjAZIqr83W1lZJ0uzZs3ltFizlzP8rki6VNLS7J9hebLvfdv/GjRvrl2yaO/fcczVr1iydc845qaMAOw0ODur555+XJD3//PNccrxgScrf9tmSXoqIteM9LyJWRURHRHS0tLTUKd30d+utt2rLli267bbbUkcBdurp6dHQUGUuODQ0pNWrVydONL2lmvm/S9K5tgckfVvSGba/lShLVgYHB9Xb26uIUG9vL7MrTBlr1qzZebnxcrmsvr6+xImmtyTlHxGfi4g5EdEm6aOS/i0iPp4iS26Gz662b9/O7ApTRmdnp5qaKleZb2pq4myfgqU+2wd1xuwKU1V3d/fOUz0bGxs526dgycs/Iu6OiLNT58gFsytMVZyJVl/Jyx/1xewKU1l3d7dOOeUUXpd1QPlnhtkVprLm5mZdc801vC7rgHv4Zqi7u1sDAwPMroCMUf4Z2jG7ApAvln0AIEOUPwBkiPIHgAxR/gCQIe8vt/WzvVHSM6lzTCNHSHo5dQhgDLw2J9exEfG6K2PuN+WPyWW7PyI6UucARuO1WR8s+wBAhih/AMgQ5Z+vVakDALvBa7MOWPMHgAwx8weADFH+AJAhyj8ztrts/9h2yfZnU+cBdrB9ve2XbD+WOksOKP+M2G6U9DeS3i/pzZLOt/3mtKmAnW6U1JU6RC4o/7y8XVIpIp6OiNckfVvSeYkzAZKkiLhH0iupc+SC8s9Lq6SfDRs/V90GIDOUPwBkiPLPy3pJxwwbz6luA5AZyj8vD0qaZ/s42wdK+qikWxNnApAA5Z+RiChL+oykf5X0hKS/j4jH06YCKmzfLOl+SSfafs72hakzTWdc3gEAMsTMHwAyRPkDQIYofwDIEOUPABmi/AEgQ5Q/MElst+24IqXtDtvXVP883/Y706YDRmpKHQCYjiKiX1J/dThf0iZJP0wWCBiFmT8gyfYXbP/E9n22b7b9R7bvtt1RffwI2wPVP7fZvtf2Q9Wv183qq7P92223Sfo9SRfbfsT2e2z/1PYB1ecdNnwM1Aszf2TP9ttUudTFqar8P/GQpLXj/MhLkhZExK9sz5N0s6SOsZ4YEQO2vyZpU0RcWT3e3ZIWSvqn6nG/FxHbJukfB6gJM39Aeo+kWyJiS0T8UhNf7+gASd+wvU7SP6hyY5w9cZ2kC6p/vkDSDXv488A+Y+YP7F5ZuyZIBw3bfrGkFyW9pfr4r/ZkpxHxH9Wlo/mSGiOC2xai7pj5A9I9kj5oe6btQyWdU90+IOlt1T9/ZNjz3yBpQ0QMSfqEpMYJ9v+qpENHbVst6e/ErB+JUP7IXkQ8JOk7kh6V9H1VLn0tSVdKusj2w5KOGPYjX5XUbftRSSdJ2jzBIW6T9KEdb/hWt90k6XBV3i8A6o6regKj2F6uYW/QFnSMj0g6LyI+UdQxgPGw5g/Ume2Vkt4v6QOpsyBfzPwBIEOs+QNAhih/AMgQ5Q8AGaL8ASBDlD8AZOj/AfZ3+aUtcJnZAAAAAElFTkSuQmCC\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEGCAYAAABiq/5QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAARTUlEQVR4nO3df5BdZX3H8c+HjZJEQEmy0nazuNqbiTqMP1fH2qHFAk6kWmoENTMKVdqMHVxWp6214qgzVaat1ppu23HSiglTTK0iIlYjwammrVR7E8GEQuWOJjRbIGtWITGAbPLtH3sXlnV/3ATOeTb7fb9mMrnPuXfv8yGzfOaZc895riNCAIA8TiodAABQL4ofAJKh+AEgGYofAJKh+AEgmUWlA3RixYoV0dfXVzoGAJxQduzY8aOI6J56/IQo/r6+PjWbzdIxAOCEYnvvdMc51QMAyVD8AJAMxQ8AyVD8AJAMxQ8AyVD8AJAMxQ8AyZwQ1/EDqNbQ0JBarVbRDMPDw5Kknp6eojkkqdFoaGBgoHSMylD8AOaFBx98sHSENCh+APNidTs4OChJ2rBhQ+EkCx/n+AEgmcqK3/bVtvfb3j3Nc39gO2yvqGp+TO/AgQO64oordODAgdJRABRS5Yp/k6Q1Uw/a7pX0akl3Vzg3ZrB582bt2rVL11xzTekoAAqprPgjYruk0Wme+itJ75HEt7zX7MCBA9q6dasiQlu3bmXVDyRV6zl+2xdKGo6I2+qcF+M2b96so0ePSpKOHDnCqh9Iqrbit71U0vskfaDD16+33bTdHBkZqTZcEjfffLPGxsYkSWNjY9q2bVvhRABKqHPF/8uSni3pNtt7JK2UtNP2L0z34ojYGBH9EdHf3f1zXyCD43Deeedp0aLxK3gXLVqk888/v3AiACXUVvwRsSsinhkRfRHRJ2mfpJdExL11Zcju0ksvffSxbV1yySUF0wAopcrLObdIukXSatv7bF9W1VzozPLly7V48WJJ0sknn6zly5cXTgSghMru3I2IdXM831fV3Jheq9XSoUOHJEmHDh1Sq9VSo9EonApA3bhzN5EPf/jDs44B5EDxJ7Jnz55ZxwByoPgT6evrm3UMIAeKP5H3v//9s44B5EDxJzL1g1w+2AVyovgTueGGGx43vvHGGwslAVASxZ/IJz7xiceNP/7xjxdKAqAkij+RiJh1DCAHih8AkqH4E5nYoG2mMYAcKP5EJvbpmWkMIAeKP5GJfXpmGgPIgeJP5JRTTnnc+NRTTy2UBEBJFH8iU1f4Bw8eLJQEQEkUPwAkQ/EDQDJcz1eToaEhtVqtohmWLVum0dHRR8fLly/X4OBgkSyNRkMDAwNF5gayY8WfSG9v7+PGK1euLJQEQEms+GsyX1a3a9eu1ejoqC6++GJdfvnlpeMAKIDiT6a3t1e9vb2UPpAYp3oAIBmKHwCSofgBIJnKit/21bb329496dif2v6e7Vtt32T7l6qaHwAwvSpX/JskrZly7KMR8YKIeJGkL0v6QIXzAwCmUVnxR8R2SaNTjj0wafg0SXwFFADUrPbLOW1/RNIlku6X9Kq65weA7Gr/cDciroyIXknXSnrnTK+zvd5203ZzZGSkvoAAsMCVvKrnWklvmOnJiNgYEf0R0d/d3V1jLABY2GotfturJg0vlHRnnfMDACo8x297i6RzJK2wvU/SByVdYHu1pKOS9kp6R1XzAwCmV1nxR8S6aQ5/qqr5AACd4c5dAEiG4geAZCh+AEiG4geAZCh+AEiG4geAZCh+AEiG4geAZCh+AEiG4geAZCh+AEiG4geAZCh+AEim9q9eBPCYoaEhtVqt0jHmhYl/h8HBwcJJ5odGo6GBgYFK3pviBwpqtVq66/bv6sxTjpSOUtxTHxk/AfHw3mbhJOXdfair0ven+IHCzjzliN73kgdKx8A8ctXO0yp9f87xA0AyFD8AJEPxA0AyFD8AJEPxA0AyFD8AJEPxA0AylRW/7att77e9e9Kxj9q+0/b3bF9v+xlVzQ8AmF6VK/5NktZMObZN0lkR8QJJ35f0JxXODwCYRmXFHxHbJY1OOXZTRIy1h/8paWVV8wMAplfyHP/bJX11pidtr7fdtN0cGRmpMRYALGxFit/2lZLGJF0702siYmNE9EdEf3d3d33hAGCBq32TNtu/I+m1ks6NiKh7fgDIrtbit71G0nsk/XpEHK5zbgDAuCov59wi6RZJq23vs32ZpL+RdKqkbbZvtf3JquYHAEyvshV/RKyb5vCnqpoPANAZ7twFgGQofgBIhuIHgGQofgBIhuIHgGQofgBIhuIHgGQofgBIhuIHgGRmvXPX9i5J022kZknR/kIVAMdpeHhYPz3Ypat2nlY6CuaRvQe79LTh4cref64tG15b2cwAgCJmLf6I2Dvx2PYZkl7WHn4nIvZXGQzIoKenRw+P3aP3veSB0lEwj1y18zSd3NNT2ft3dI7f9hslfUfSxZLeKOnbti+qLBUAoDKd7s55paSXTazybXdLulnS56sKBgCoRqdX9Zw05dTOgWP4WQDAPNLpin+r7a9J2tIev0nSV6qJBACoUkfFHxF/ZPsNkn61fWhjRFxfXSwAQFU6/gauiLhO0nUVZgEA1KDTq3rW2r7L9v22H7B90DbXnwHACajTFf9fSHpdRNxRZRgAQPU6vTLnPkofABaGufbqWdt+2LT9WUlflPTwxPMR8YUKswEAKjDXqZ7XTXp8WNKrJ41DEsUPACeYufbqedvxvrHtqzW+ydv+iDirfexiSR+S9DxJL4+I5vG+PwDg+HR6Vc9K29fb3t/+c53tlXP82CZJa6Yc2y1praTtxx4VAPBk6PSqnk9L+ozGN2mTpLe0j50/0w9ExHbbfVOO3SFJto815xMyNDSkVqtV65zz1cS/w+DgYOEk80Oj0dDAwEDpGECtOi3+7oj49KTxJtvvqiLQBNvrJa2XpDPPPPMJvVer1dKtu+/QkaXLnoxoJ7STfjb+vTo7fnBf4STldR0eLR0BKKLT4j9g+y16bK+edRrfqK0yEbFR0kZJ6u/vn+5bwI7JkaXL9OBzL3jCubBwLLmT7aaQU6fX8b9d4/vw3yvpHkkXSTruD34BAOV0uknbXkm/VXEWAEANOr2qZ7PtZ0wan96+XHO2n9ki6RZJq23vs32Z7dfb3ifpVyT9S3urZwBAjTo9x/+CiPjJxCAifmz7xbP9QESsm+EptnMGgII6/gYu26dPDGwv0zFs6QwAmD86Le+/lHSL7c9JssY/3P1IZakAAJXp9MPda2w3Jf1G+9DaiPjv6mIBAKoy1+6ck+94ulfjd+8++lxEcAcM8ATdfahLV+08rXSM4u47PH7m+YylRwsnKe/uQ11aVeH7z7Xi36HxXTgn9liYuJHK7cfPqSgXkEKj0SgdYd74WXs7kZOfxb/JKlX7uzHX7pzPnnjcXv2vkrS4sjRAMuwT9JiJ/aM2bNhQOMnC19E5ftu/K2lQ0kpJt0p6haRvSTq3umgAgCp0ejnnoKSXSdobEa+S9GJJ91eWCgBQmU6L/6GIeEiSbJ8cEXdKWl1dLABAVTq9jn9fe8uGL0raZvvHkvZWFwsAUJVOr+N/ffvhh2z/q6SnS9paWSoAQGWOeduFiPhmFUEAAPXo9Bw/AGCBoPgBIBmKHwCSofgBIBmKHwCSofgBIBmKHwCSofgBIBmKHwCSofgBIBmKHwCSqaz4bV9te7/t3ZOOLbO9zfZd7b9Pr2p+AMD0qlzxb5K0Zsqx90r6ekSskvT19hgAUKNj3p2zUxGx3XbflMMXSjqn/XizpG9I+uOqMkwYHh5W1+H7teTOr1Q9FU4gXYcPaHh4rHQMoHZ1n+M/IyLuaT++V9IZM73Q9nrbTdvNkZGRetIBQAKVrfjnEhFhO2Z5fqOkjZLU398/4+s60dPTo3sfXqQHn3vBE3kbLDBL7vyKenpmXHsAC1bdK/77bP+iJLX/3l/z/ACQXt3F/yVJl7YfXyrphprnB4D0qrycc4ukWySttr3P9mWS/kzS+bbvknReewwAqFGVV/Wsm+Gpc6uaEwAwN+7cBYBkKH4ASIbiB4BkKH4ASIbiB4BkKH4ASIbiB4BkKH4ASIbiB4BkKH4ASIbiB4BkKH4ASKbYF7HUrevwKF+9KOmkhx6QJB1dfFrhJOV1HR7VLF8CByxYKYq/0WiUjjBvtFoHJUmN51B40hn8biClFMU/MDBQOsK8MTg4KEnasGFD4SQASuEcPwAkQ/EDQDIUPwAkQ/EDQDIUPwAkQ/EDQDIUPwAkQ/EDQDJFit/2oO3dtm+3/a4SGQAgq9qL3/ZZkn5P0sslvVDSa21z3zwA1KTEiv95kr4dEYcjYkzSNyWtLZADAFIqUfy7JZ1te7ntpZIukNQ79UW219tu2m6OjIzUHhIAFqraiz8i7pD055JukrRV0q2Sjkzzuo0R0R8R/d3d3TWnBICFq8iHuxHxqYh4aUT8mqQfS/p+iRwAkFGRbZltPzMi9ts+U+Pn919RIgcAZFRqP/7rbC+X9IikyyPiJ4VyAEA6RYo/Is4uMS8AgDt3ASAdih8AkqH4ASAZih8AkqH4ASAZih8AkqH4ASAZih8AkqH4ASCZUls2AJhHhoaG1Gq1imaYmH9wcLBoDklqNBoaGBgoHaMyFD+AeWHJkiWlI6RB8QNY0Ktb/DzO8QNAMhQ/ACRD8QNAMhQ/ACRD8QNAMhQ/ACRD8QNAMhQ/ACRD8QNAMhQ/ACRD8QNAMkWK3/a7bd9ue7ftLbYXl8gBABnVXvy2eyRdIak/Is6S1CXpzXXnAICsSu3OuUjSEtuPSFoq6f8K5ajNfNjvXJo/e54v9P3Ogfms9hV/RAxL+pikuyXdI+n+iLhp6utsr7fdtN0cGRmpO+aCtWTJEvY9B5JzRNQ7oX26pOskvUnSTyR9TtLnI+IfZ/qZ/v7+aDabNSUEgIXB9o6I6J96vMSHu+dJ+mFEjETEI5K+IOmVBXIAQEoliv9uSa+wvdS2JZ0r6Y4COQAgpRLn+L8t6fOSdkra1c6wse4cAJBVkat6IuKDkj5YYm4AyI47dwEgGYofAJKh+AEgGYofAJKp/Qau42F7RNLe0jkWkBWSflQ6BDANfjefXM+KiO6pB0+I4seTy3Zzurv5gNL43awHp3oAIBmKHwCSofhz4k5pzFf8btaAc/wAkAwrfgBIhuIHgGQo/kRsr7H9P7Zbtt9bOg8wwfbVtvfb3l06SwYUfxK2uyT9raTXSHq+pHW2n182FfCoTZLWlA6RBcWfx8sltSLiBxHxM0n/JOnCwpkASVJEbJc0WjpHFhR/Hj2S/nfSeF/7GIBkKH4ASIbiz2NYUu+k8cr2MQDJUPx5/JekVbafbfupkt4s6UuFMwEogOJPIiLGJL1T0tck3SHpnyPi9rKpgHG2t0i6RdJq2/tsX1Y600LGlg0AkAwrfgBIhuIHgGQofgBIhuIHgGQofgBIhuIHngS2+yZ2lrTdb/uv24/Psf3KsumAx1tUOgCw0EREU1KzPTxH0iFJ3yoWCJiCFT/Ss32l7e/b/nfbW2z/oe1v2O5vP7/C9p724z7b/2Z7Z/vPz63m26v8L9vuk/QOSe+2favts23/0PZT2q87bfIYqAsrfqRm+6Ua377iRRr//2GnpB2z/Mh+SedHxEO2V0naIql/uhdGxB7bn5R0KCI+1p7vG5J+U9IX2/N+ISIeeZL+c4COsOJHdmdLuj4iDkfEA5p7/6KnSPp727skfU7jX2pzLP5B0tvaj98m6dPH+PPAE8aKH5jemB5bGC2edPzdku6T9ML28w8dy5tGxH+0TxedI6krIviqQdSOFT+y2y7pt20vsX2qpNe1j++R9NL244smvf7pku6JiKOS3iqpa473Pyjp1CnHrpH0GbHaRyEUP1KLiJ2SPivpNklf1fj21ZL0MUm/b/u7klZM+pG/k3Sp7dskPVfST+eY4kZJr5/4cLd97FpJp2v88wGgduzOCUxi+0Oa9GFsRXNcJOnCiHhrVXMAs+EcP1Aj20OSXiPpgtJZkBcrfgBIhnP8AJAMxQ8AyVD8AJAMxQ8AyVD8AJDM/wPu7xIUVlQk0wAAAABJRU5ErkJggg==\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"From the obtained boxplots, it would appear that 'alcohol', 'density' and 'total_sulfur_dioxide' are the three most powerful predictors. The remaining predictors look relatively weaker."
],
"metadata": {
"id": "6ZNgidDjWSRb",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"# Logisitic Regression"
],
"metadata": {
"id": "581Gr2wcW8qt",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**4) Select 'quality' as the target variable and 'density' and 'alcohol' as the predictors. Fit a logistic regression model to the data, and output its summary.**\n",
"\n",
"**How do you interpret the obtained coefficients ? Are they significant ? What does it tell you ?** \n",
"\n",
"**Use the \"Logit\" model of the 'statsmodel' library, and create your input matrices using the method 'dmatrices' from the 'patsy' library. Do not split the dataset.**"
],
"metadata": {
"id": "6gqAkSWiXOm1",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"y, X = dmatrices('quality ~ density + alcohol', data=df, return_type='dataframe')\n",
"\n",
"'''\n",
"If you don't want to use the method dmatrices and directly select the columns in the dataframe, you must be careful as statsmodel does not fit an \n",
"intercept by default. In this case, you must add a constant column to the input X (using the method add_constant) that will be used to fit an intercept. \n",
"\n",
"y = df.quality\n",
"X = df[['density', 'alcohol']]\n",
"X =sm.tools.tools.add_constant(X)\n",
"'''\n",
"log_reg = sm.Logit(y, X).fit()\n",
"\n",
"print(log_reg.summary())"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "6jZW_2WrRtsu",
"outputId": "9c7e7c29-5922-4cef-8cd6-2ffb466f454e",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": 48,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0 0\n",
"1 0\n",
"2 0\n",
"3 0\n",
"4 0\n",
" ..\n",
"4893 0\n",
"4894 0\n",
"4895 0\n",
"4896 1\n",
"4897 0\n",
"Name: quality, Length: 4898, dtype: int64\n",
" const density alcohol\n",
"0 1.0 1.00100 8.8\n",
"1 1.0 0.99400 9.5\n",
"2 1.0 0.99510 10.1\n",
"3 1.0 0.99560 9.9\n",
"4 1.0 0.99560 9.9\n",
"... ... ... ...\n",
"4893 1.0 0.99114 11.2\n",
"4894 1.0 0.99490 9.6\n",
"4895 1.0 0.99254 9.4\n",
"4896 1.0 0.98869 12.8\n",
"4897 1.0 0.98941 11.8\n",
"\n",
"[4898 rows x 3 columns]\n",
"Optimization terminated successfully.\n",
" Current function value: 0.448364\n",
" Iterations 7\n",
" Logit Regression Results \n",
"==============================================================================\n",
"Dep. Variable: quality No. Observations: 4898\n",
"Model: Logit Df Residuals: 4895\n",
"Method: MLE Df Model: 2\n",
"Date: Thu, 31 Mar 2022 Pseudo R-squ.: 0.1416\n",
"Time: 14:39:53 Log-Likelihood: -2196.1\n",
"converged: True LL-Null: -2558.4\n",
"Covariance Type: nonrobust LLR p-value: 4.527e-158\n",
"==============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"const -26.5689 20.634 -1.288 0.198 -67.011 13.873\n",
"density 16.5253 20.370 0.811 0.417 -23.399 56.449\n",
"alcohol 0.8192 0.048 16.903 0.000 0.724 0.914\n",
"==============================================================================\n"
]
},
{
"output_type": "stream",
"name": "stderr",
"text": [
"/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:117: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
" x = pd.concat(x[::order], 1)\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"The logistic regression model can be made linear by taking the log() of the odds :\n",
"\n",
"$\\text{log}\\Big(\\frac{P(Y=1|X;\\beta)}{1- P(Y=1|X;\\beta)}\\Big) = \\beta_0 + \\beta_1*\\text{density} + \\beta_2*\\text{alcohol}$\n",
"\n",
"For a fixed value of 'density', a unit increase of 'alcohol' increases the **log_odds** of having a superior quality wine by 0.82, or equivalently, it increases the **odds** by e^(0.82) = 2.27.\n",
"\n",
"The same reasoning applies for the variable 'density'. Here, the intercept does not have an interpretation, as the variable 'density' cannot take on the value 0. \n",
"\n",
"Looking at its p-value, the coefficient of the variable 'density' is not significant at the 5% significance level, which means that there's not enough evidence in the data to conclude of a significant relationship between the variables 'density' and 'quality'.\n",
"On the other hand, the coefficient of the variable 'alcohol' is significant at the 5% significance level, which allows us to reject the null-hypothesis that this coefficient equals 0. Thus, we can conlude that there exits a relationship between the alcohol degree and the quality of the wine.\n"
],
"metadata": {
"id": "LUFNKDO-YqgP",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**5) Refit the same model as above, but introduce an interaction term between the variables 'density' and 'alcohol'.**\n",
"\n",
"**How do you interpret the model ? What happened to the significance of the coefficients ?**"
],
"metadata": {
"id": "oD0tI8w-bOcC",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"y, X = dmatrices('quality ~ density*alcohol', data=df, return_type='dataframe')\n",
"\n",
"log_reg = sm.Logit(y, X).fit()\n",
"\n",
"print(log_reg.summary())\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "LN6B0eigOkZI",
"outputId": "d46e6166-46fb-417a-b74f-a19e29b5e14b",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 0.446403\n",
" Iterations 9\n",
" Logit Regression Results \n",
"==============================================================================\n",
"Dep. Variable: quality No. Observations: 4898\n",
"Model: Logit Df Residuals: 4894\n",
"Method: MLE Df Model: 3\n",
"Date: Thu, 31 Mar 2022 Pseudo R-squ.: 0.1454\n",
"Time: 11:39:53 Log-Likelihood: -2186.5\n",
"converged: True LL-Null: -2558.4\n",
"Covariance Type: nonrobust LLR p-value: 6.651e-161\n",
"===================================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-----------------------------------------------------------------------------------\n",
"Intercept -540.7432 118.011 -4.582 0.000 -772.040 -309.447\n",
"density 534.4311 118.809 4.498 0.000 301.571 767.292\n",
"alcohol 49.5531 11.215 4.419 0.000 27.572 71.534\n",
"density:alcohol -49.0989 11.302 -4.344 0.000 -71.250 -26.948\n",
"===================================================================================\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"All the coefficients of the model are now statistically significant at the 5% significance level. \n",
"\n",
"The model now writes : $\\text{log}\\Big(\\frac{P(Y=1|X;\\beta)}{1- P(Y=1|X;\\beta)}\\Big) = \\beta_0 + \\text{alcohol}*(\\beta_1 + \\beta_3*\\text{density}) + \\beta_2*\\text{density}$ \n",
"\n",
"Thus, by keeping 'density' constant, a unit increase in 'alcohol' increases the log_odds by : $534.43 - 49.1*\\text{density}$. The same reasoning applies for the variable 'density'.\n"
],
"metadata": {
"id": "RC3Egd4ibney",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"# Linear Discriminant Analysis"
],
"metadata": {
"id": "n-J7MIIGgkBj",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**6) Select the predictor variable 'density' and fit a LDA model to classify the target variable 'quality'. Do not split the dataset.**\n",
"\n",
"**Compute the decision boundary of the model. Then, on the same plot, display the densities of the variable 'density' for each class of 'quality' scaled by their priors, as well as the decision boundary. What do you observe ?**\n",
"\n",
"**You can draw a normal distribution using the method 'norm.pdf' from the 'scipy' library. Check the attributes of the class 'LDA' to see how you can obtain the priors, the means, and the variance**"
],
"metadata": {
"id": "BSzFQjOagfDM",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"X = df[\"density\"].values[:,np.newaxis]\n",
"#X = df.drop(\"quality\", axis=1)\n",
"y = df.quality \n",
"\n",
"model = LinearDiscriminantAnalysis(store_covariance=True)\n",
"\n",
"model.fit(X,y)\n",
"\n",
"mean1, mean2 = model.means_[0,0], model.means_[1,0]\n",
"variance = model.covariance_[0,0]\n",
"\n",
"p1 , p2 = model.priors_[0], model.priors_[1]\n",
"\n",
"scaled_mean1, scaled_mean2 = mean1*p1, mean2*p2\n",
"scaled_variance1, scaled_variance2 = variance*(p1**2), variance*(p2**2)\n",
"\n",
"decision_boundary = (mean1 + mean2)/2 + variance/(mean1-mean2)*np.log(p2/p1)\n",
"print(decision_boundary)\n",
"\n",
"fig, ax = plt.subplots()\n",
"x_axis = np.arange(0.95, 1.05, 0.0001)\n",
"\n",
"ax.plot(x_axis, p1*norm.pdf(x_axis,mean1,math.sqrt(variance)), color='red', label='class 1')\n",
"ax.plot(x_axis, p2*norm.pdf(x_axis,mean2,math.sqrt(variance)), color='blue', label='class 0')\n",
"ax.axvline(decision_boundary, color='green', label='boundary')\n",
"ax.legend()\n",
"fig.set_size_inches(18.5, 10.5)\n",
"plt.show()\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 637
},
"id": "N9cD5dR3HyOt",
"outputId": "591974d5-19eb-4939-8df2-a4191b829ee1",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.9883104940894065\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1332x756 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"by writting the variable 'density' as x, the boundary decision for a LDA is computed as such :\n",
"\n",
"$\\delta_0(x) = \\delta_1(x)$\n",
"\n",
"$\\leftrightarrow x\\frac{\\mu_0}{\\sigma^2} - \\frac{\\mu_0^2}{2\\sigma^2} + \\text{log}(\\pi_0) = x\\frac{\\mu_1}{\\sigma^2} - \\frac{\\mu_1^2}{2\\sigma^2} + \\text{log}(\\pi_1) $\n",
"\n",
"$\\leftrightarrow x(\\frac{\\mu_0 - \\mu_1}{\\sigma^2}) = \\frac{\\mu_0^2 - \\mu_1^2}{2\\sigma^2} + \\text{log}(\\frac{\\pi_1}{\\pi_0})$ \n",
"\n",
"$\\leftrightarrow x = \\frac{\\mu_0 + \\mu_1}{2} + \\frac{\\sigma^2}{\\mu_0 - \\mu_1}\\text{log}(\\frac{\\pi_1}{\\pi_0})$\n",
"\n",
"\n",
"If we plot $\\pi_0f_0(x)$, $\\pi_1f_1(x)$, we can observe that the decision boundary falls right at the intersection of the two scaled density functions. This is indeed expected as the LDA classifier will classify an observation to the class '0' or to the class '1' based on :\n",
"\n",
"$p_k(x) = \\underset{k \\in {0,1}}{\\text{argmax}} \\frac{\\pi_kf_k(x)}{\\sum_{l \\in {0,1}} \\pi_l f_l(x)} = \\underset{k \\in {0,1}}{\\text{argmax}}~\\pi_kf_k(x)$, as the denominator is constant $∀k$. \n",
"\n",
"\n",
"The boundary decision tells us how the LDA classifier will classify a wine based on its density value. In this case, for any value of density below 0.988, the wine will be classified as inferior (0), and as superior (1) for any value of density above 0.988. \n"
],
"metadata": {
"id": "mG3EBm40h5YN",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**7) Select the variables 'sulphate' and 'alcohol' as predictor variables, and fit a LDA model to predict the variable 'quality'. Do not split the dataset.**\n",
"\n",
"**Draw a scatter plot of the predictor variables, while separating for the class 'quality'. Then, on the predictor space, draw the decision boundary.** \n",
"\n",
"**Check how you can obtain the 'coefficients' and the 'intercept' for the decision boundary [here](https://scikit-learn.org/stable/modules/lda_qda.html#lda-qda-math) and [here](https://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html).**"
],
"metadata": {
"id": "SesMStXDifcz",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"X = df[['sulphates', 'alcohol']]\n",
"y = df.quality\n",
"\n",
"colors = {0:'red', 1:'green'}\n",
"\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.scatter(X['sulphates'], X['alcohol'], c=y.map(colors))\n",
"fig.set_size_inches(18.5, 10.5)\n",
"\n",
"model.fit(X,y)\n",
"\n",
"covariance = model.covariance_\n",
"mean1, mean2 = model.means_[0], model.means_[1]\n",
"\n",
"w1, w2 = model.coef_[0][0], model.coef_[0][1]\n",
"intercept = model.intercept_[0]\n",
"\n",
"x1 = np.arange(0, 1.2, 0.001)\n",
"x2 = (-intercept - w1*x1)/w2\n",
"\n",
"ax.plot(x1, x2, color='blue', label='Decision boundary')\n",
"ax.legend()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 637
},
"id": "6ToaKHeQa_hZ",
"outputId": "c4c8e47d-1d1f-4180-cb44-29b1e291b212",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcf00e59ad0>"
]
},
"metadata": {},
"execution_count": 40
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1332x756 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"The LDA classifier being a linear model, its decision boundary is a straight line in two dimensions. In the above scatter plot, we can observe that the observations are not linearly separable, which means that we cannot find a straight line that perfectly splits the two classes. \n",
"\n",
"Intuitively, you might think that we should be better off if we could find a complex polynomial function that could perfectly separate all of my points (which would result in a training error of 0). However, by doing so, we'll also model the 'noise' in the data, and if we tried to apply this model to a new dataset (unseen by the model during training), it will likely result in a high error. "
],
"metadata": {
"id": "MQuHb5l-KOZr",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"# Classifiers comparison and metrics"
],
"metadata": {
"id": "DJVsvu8GkF2P",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**8) Using the three most powerful predictors identified in exercice 3, successively fit a logistic regression model, a LDA, a QDA, and a Naïve Bayes model to predict the target variable 'quality' using a 10-folds cross-validation. Evaluate the model on its accuracy.**\n",
"\n",
"**For convergence issue, set the logistic regression solver to 'liblinear', and fit the intercept. The Gaussian Naïve Bayes classifier is called 'GaussianNB' is scikit-learn.**\n",
"\n",
"**Which of the four classifiers performs best in classifying the target variable 'quality' ?**\n"
],
"metadata": {
"id": "65ahG9PUkA8h",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"X = df[['alcohol', 'density', 'total_sulfur_dioxide']]\n",
"y = df.quality\n",
"\n",
"model_lr = LogisticRegression(fit_intercept=True, solver='liblinear')\n",
"model_lda = LinearDiscriminantAnalysis()\n",
"model_qda = QuadraticDiscriminantAnalysis()\n",
"model_bayes = GaussianNB() \n",
"\n",
"cv_results_lr = cross_validate(model_lr, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"cv_results_lda = cross_validate(model_lda, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"cv_results_qda = cross_validate(model_qda, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"cv_results_bayes = cross_validate(model_bayes, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"\n",
"\n",
"train_acc_lr = cv_results_lr['train_accuracy']\n",
"test_acc_lr = cv_results_lr['test_accuracy']\n",
"mean_train_acc_lr = train_acc_lr.mean()\n",
"mean_test_acc_lr = test_acc_lr.mean()\n",
"\n",
"train_acc_lda = cv_results_lda['train_accuracy']\n",
"test_acc_lda = cv_results_lda['test_accuracy']\n",
"mean_train_acc_lda = train_acc_lda.mean()\n",
"mean_test_acc_lda = test_acc_lda.mean()\n",
"\n",
"train_acc_qda = cv_results_qda['train_accuracy']\n",
"test_acc_qda = cv_results_qda['test_accuracy']\n",
"mean_train_acc_qda = train_acc_qda.mean()\n",
"mean_test_acc_qda = test_acc_qda.mean()\n",
"\n",
"train_acc_bayes = cv_results_bayes['train_accuracy']\n",
"test_acc_bayes = cv_results_bayes['test_accuracy']\n",
"mean_train_acc_bayes = train_acc_bayes.mean()\n",
"mean_test_acc_bayes = test_acc_bayes.mean()\n",
"\n",
"print('Train accuracy for Logistic Regression: {}'.format(mean_train_acc_lr))\n",
"print('Test accuracy for Logistic Regression: {}'.format(mean_test_acc_lr))\n",
"\n",
"print('Train accuracy for LDA: {}'.format(mean_train_acc_lda))\n",
"print('Test accuracy for LDA: {}'.format(mean_test_acc_lda))\n",
"\n",
"print('Train accuracy for QDA: {}'.format(mean_train_acc_qda))\n",
"print('Test accuracy for QDA: {}'.format(mean_test_acc_qda))\n",
"\n",
"print('Train accuracy for Naive Bayes: {}'.format(mean_train_acc_bayes))\n",
"print('Test accuracy for Naive Bayes: {}'.format(mean_test_acc_bayes))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "ZTPecde9HjyV",
"outputId": "768e2a5f-5bcd-4408-9e78-1f04f87b466d",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Train accuracy for Logistic Regression: 0.7989655501718766\n",
"Test accuracy for Logistic Regression: 0.7960368932849213\n",
"Train accuracy for LDA: 0.7952905169635283\n",
"Test accuracy for LDA: 0.7913288260089312\n",
"Train accuracy for QDA: 0.7973321820694267\n",
"Test accuracy for QDA: 0.7923504862067527\n",
"Train accuracy for Naive Bayes: 0.7795471562663238\n",
"Test accuracy for Naive Bayes: 0.7782546638287215\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"The classifiers results are very close to one another, but the logistic regression model seems to be generalizing best. "
],
"metadata": {
"id": "zRWIvZmxlQtT",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**9) Perform the same experiment as the previous point, but now include all predictor variables. Do you notice a significant gain in performance ?**"
],
"metadata": {
"id": "jmguu_kQldFh",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"X = df.drop('quality', axis=1)\n",
"y = df.quality\n",
"\n",
"model_lr = LogisticRegression(fit_intercept=True, solver='liblinear')\n",
"model_lda = LinearDiscriminantAnalysis()\n",
"model_qda = QuadraticDiscriminantAnalysis()\n",
"model_bayes = GaussianNB() \n",
"\n",
"cv_results_lr = cross_validate(model_lr, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"cv_results_lda = cross_validate(model_lda, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"cv_results_qda = cross_validate(model_qda, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"cv_results_bayes = cross_validate(model_bayes, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
"\n",
"\n",
"train_acc_lr = cv_results_lr['train_accuracy']\n",
"test_acc_lr = cv_results_lr['test_accuracy']\n",
"mean_train_acc_lr = train_acc_lr.mean()\n",
"mean_test_acc_lr = test_acc_lr.mean()\n",
"\n",
"train_acc_lda = cv_results_lda['train_accuracy']\n",
"test_acc_lda = cv_results_lda['test_accuracy']\n",
"mean_train_acc_lda = train_acc_lda.mean()\n",
"mean_test_acc_lda = test_acc_lda.mean()\n",
"\n",
"train_acc_qda = cv_results_qda['train_accuracy']\n",
"test_acc_qda = cv_results_qda['test_accuracy']\n",
"mean_train_acc_qda = train_acc_qda.mean()\n",
"mean_test_acc_qda = test_acc_qda.mean()\n",
"\n",
"train_acc_bayes = cv_results_bayes['train_accuracy']\n",
"test_acc_bayes = cv_results_bayes['test_accuracy']\n",
"mean_train_acc_bayes = train_acc_bayes.mean()\n",
"mean_test_acc_bayes = test_acc_bayes.mean()\n",
"\n",
"print('Train accuracy for Logistic Regression: {}'.format(mean_train_acc_lr))\n",
"print('Test accuracy for Logistic Regression: {}'.format(mean_test_acc_lr))\n",
"\n",
"print('Train accuracy for LDA: {}'.format(mean_train_acc_lda))\n",
"print('Test accuracy for LDA: {}'.format(mean_test_acc_lda))\n",
"\n",
"print('Train accuracy for QDA: {}'.format(mean_train_acc_qda))\n",
"print('Test accuracy for QDA: {}'.format(mean_test_acc_qda))\n",
"\n",
"print('Train accuracy for Naive Bayes: {}'.format(mean_train_acc_bayes))\n",
"print('Test accuracy for Naive Bayes: {}'.format(mean_test_acc_bayes))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "1wUctrK4rSdg",
"outputId": "de078e87-7572-4224-a63a-56c3a9abdd53",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Train accuracy for Logistic Regression: 0.8017557100453248\n",
"Test accuracy for Logistic Regression: 0.7962351320896457\n",
"Train accuracy for LDA: 0.8024362496444535\n",
"Test accuracy for LDA: 0.7964346229289261\n",
"Train accuracy for QDA: 0.7547070029583935\n",
"Test accuracy for QDA: 0.7394628771754099\n",
"Train accuracy for Naive Bayes: 0.727984074194057\n",
"Test accuracy for Naive Bayes: 0.7261821292934352\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"The performance of the logisitic regression model and of the LDA only marginally increased, while it even decreased for the QDA and Naïve Bayes models. This may indicate that the remaining predictors do not have a strong discriminative power in predicting the outcome variable. "
],
"metadata": {
"id": "nrZMtf6vlrwZ",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**10) Select the best model found above and the 3 most relevant predictors, split your data in train and test datasets according to a 0.8/0.2 partition, and fit it to the training data.** \n",
"\n",
"**Evaluate the model on the accuracy, and display the confusion matrix. You'll need to use the 'confusion_matrix' and the 'ConfusionMatrixDisplay' methods from the scikit-learn library. Can you think of any problem that might arise when evaluating the model on the accuracy ? Think of the distribution of the target variable.**"
],
"metadata": {
"id": "eHttmMLtpmBp",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "markdown",
"source": [
"**11) Compute the True Positive Rate, the True Negative Rate, the False Positive Rate, the False Negative Rate, and the Precision. How do you interpret these metrics ? The TP, FP, TN and FN can be directly obtained from the confusion matrix.**\n",
"\n",
"**Draw the Receiver Operating Curve, and compute the area under the curve. You'll need the methods 'roc_curve' and 'roc_auc_score'. Does the model look to have any predictive power ?**"
],
"metadata": {
"id": "50WC2stNqs1R",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"X = df[['alcohol', 'density', 'total_sulfur_dioxide']]\n",
"y = df.quality\n",
"\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.8)\n",
"\n",
"model_lr.fit(X_train, y_train)\n",
"y_pred = model_lr.predict(X_test)\n",
"\n",
"cm = confusion_matrix(y_test, y_pred)\n",
"\n",
"disp = ConfusionMatrixDisplay(confusion_matrix=cm)\n",
"disp.plot()\n",
"\n",
"tn, fp, fn, tp = cm.ravel()\n",
"\n",
"tp_rate = tp/(tp + fn)\n",
"fp_rate = fp/(tn + fp )\n",
"tn_rate = tn/(tn + fp)\n",
"fn_rate = fn/(tp + fn)\n",
"precision = tp/(tp+fp)\n",
"\n",
"\n",
"print('TPR : {}'.format(tp_rate))\n",
"print('FPR : {}'.format(fp_rate))\n",
"print('TNR : {}'.format(tn_rate))\n",
"print('FNR : {}'.format(fn_rate))\n",
"print('Precision : {}'.format(precision))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 368
},
"id": "L3Mk0kRxZcl1",
"outputId": "6da2b7f4-fe38-42ea-dbb9-c4e067a06c7f",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"TPR : 0.2376237623762376\n",
"FPR : 0.02699228791773779\n",
"TNR : 0.9730077120822622\n",
"FNR : 0.7623762376237624\n",
"Precision : 0.6956521739130435\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"We have an imbalanced dataset, with onlt 22% of observations belonging to the positive class. Let's say our classifier only classify observations to the negative class. In this case, the accuracy is : $\\text{Acc} = \\frac{TP + TN}{N + P} = 0 + 0.78 = 0.78$. This means that, even if the model can only predict the '0' class, we'll get an accuracy of 78%, which can be highly misleading regarding the performance of the model. The confusion matrix can give more insight regarding what's really happening behind the scenes. \n",
"\n",
"$TPR = \\frac{TP}{TP + FN} = 0.19$\n",
"* Amongst all the observations belonging the positive class, only 19% were correctly classified as positive. \n",
"\n",
"$FPR = \\frac{FP}{TN + FP} = 0.02$ \n",
"* Amongst all the observations belonging to the negative class, only 2% were wrongly classified as positive.\n",
"\n",
"$TNR = \\frac{TN}{TN + FP} = 0.98$\n",
"* Amongst all the observations belonging to the negative class, 98% were correctly classified as negative. \n",
"\n",
"$FNR = \\frac{FN}{FN + TP} = 0.81$\n",
"* Amongst all the observations belonging to the positive class, 81% were wrongly classified as negative.\n",
"\n",
"$\\text{Precision} = \\frac{TP}{TP + FP} = 0.68$\n",
"* Amongst all the observations that were classified by the model as positive, \n",
"68% are actually positive. \n",
"\n",
"\n",
"The FNR is very high, meaning that our model has the tendency to classify positive instances as negatives. This behaviour can be explained by the high class imbalance present in the dataset. "
],
"metadata": {
"id": "-0VuZoM9ruzY",
"pycharm": {
"name": "#%% md\n"
}
}
},
{
"cell_type": "code",
"source": [
"y_score = model_lr.predict_proba(X_test)[:,1]\n",
"fpr, tpr, thresholds = roc_curve(y_test, y_score, pos_label=1)\n",
"\n",
"fig, ax = plt.subplots()\n",
"fig.set_size_inches(8, 8)\n",
"\n",
"xaxis = np.arange(0,1.1,0.1)\n",
"\n",
"ax.plot(xaxis, xaxis, label='Baseline')\n",
"ax.set_xlabel('False Positive Rate')\n",
"ax.set_ylabel('True Positive Rate')\n",
"\n",
"roc_auc = roc_auc_score(y_test, y_score) \n",
"\n",
"ax.plot(fpr, tpr, label='ROC curve (AUROC = {}'.format(roc_auc))\n",
"ax.legend()\n",
"ax.set_title('Receiver Operating Curvee')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 531
},
"id": "qFQy0MpyrsBQ",
"outputId": "fb25d8a5-aae8-44e6-8dcd-6b083c2276f0",
"pycharm": {
"name": "#%%\n"
}
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Receiver Operating Curvee')"
]
},
"metadata": {},
"execution_count": 44
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"A random model (i.e. a model that classifies observations randomly, meaning it has no predictive power) will have a AUC of 0.5, represented here by the blue line. As the AUC reaches 0.77, and as the ROC is clearly above the baseline, we can conclude that the model has indeed predictive power. \n",
"\n",
"Adjusting for the threshold depends on the application at hand, and on the objective that we want to maximize. If capturing positive instances is more important than wrongly classifying negatives as positives, we'll increase the threshold. On the other hand, if we want to keep the FPR at a bare minimum, we'll decrease the threshold. Its a question of compromise.\n",
"\n",
"As a side note, the AUROC can get below 0.5, meaning that the model performs even worse than a random classifier. "
],
"metadata": {
"id": "9A0UbxO1wRI5",
"pycharm": {
"name": "#%% md\n"
}
}
}
]
}