TP-ML/ex/Lab9_exercises.ipynb

{
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 "metadata": {
  "colab": {
   "name": "Lab9_exercises",
   "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": 39,
   "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 = '../data/wine.csv'\n",
    "\n",
    "##Read dataframe##\n",
    "\n",
    "df = pd.read_csv(file,index_col=0)\n",
    "#df= df.astype({'quality':'category'})\n",
    "\n",
    "\n",
    "print(df.head())\n",
    "print(df.info())\n",
    "print(df.isna().sum())"
   ],
   "metadata": {
    "id": "zKQyTrqKZLmg",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 43,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   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",
      "<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           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": [
    "sns.countplot(x='quality', data=df, order = df.quality.value_counts().index)\n",
    "plt.show()"
   ],
   "metadata": {
    "id": "oYULnCz6ZVmu",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 44,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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5I8DZwMo2nQpcD5ya5FjgCmAcKGBrkk1V9UyPfUsL3v++6u+PugUtQG/5t/f3tu/eziyq6hvA7v3Ka4CNbX4jcO5Q/aYauBM4OskJwFnAlqra3QJiC7C6r54lSdOb73sWx1fVzjb/JHB8m18KPDE0bnurzVSXJM2jkd3grqpicGlpTiRZl2QiycTU1NRc7VaSxPyHxVPt8hLt565W3wEsHxq3rNVmqr9KVa2vqvGqGh8bG5vzxiVpMZvvsNgE7HuiaS1w21D9wvZU1GnAs+1y1e3AmUmOaU9OndlqkqR51NvTUEluBk4HjkuyncFTTR8Hbk1yMfA94P1t+GbgHGASeBG4CKCqdif5KHBPG3dVVe1/01yS1LPewqKqLphh1bunGVvAJTPsZwOwYQ5bkyQdJD/BLUnqZFhIkjoZFpKkToaFJKmTYSFJ6mRYSJI6GRaSpE6GhSSpk2EhSepkWEiSOhkWkqROhoUkqZNhIUnqZFhIkjoZFpKkToaFJKmTYSFJ6mRYSJI6jSQskjye5P4k25JMtNqxSbYk+W77eUyrJ8knk0wmuS/JO0bRsyQtZqM8s/jHVbWqqsbb8mXAHVW1ErijLQOcDaxs0zrg+nnvVJIWuYV0GWoNsLHNbwTOHarfVAN3AkcnOWEE/UnSojWqsCjgvyTZmmRdqx1fVTvb/JPA8W1+KfDE0LbbW02SNE8OG9Fx/1FV7Ujyt4AtSf5qeGVVVZI6mB220FkH8Ja3vGXuOpUkjebMoqp2tJ+7gC8DpwBP7bu81H7uasN3AMuHNl/Wavvvc31VjVfV+NjYWJ/tS9KiM+9hkeRvJjlq3zxwJvAAsAlY24atBW5r85uAC9tTUacBzw5drpIkzYNRXIY6Hvhykn3H/6Oq+s9J7gFuTXIx8D3g/W38ZuAcYBJ4Ebho/luWpMVt3sOiqh4F3j5N/Wng3dPUC7hkHlqTJM1gIT06K0laoAwLSVInw0KS1MmwkCR1MiwkSZ0MC0lSJ8NCktTJsJAkdTIsJEmdDAtJUifDQpLUybCQJHUyLCRJnQwLSVInw0KS1MmwkCR1MiwkSZ0MC0lSp0MmLJKsTvJIkskkl426H0laTA6JsEiyBPg0cDZwEnBBkpNG25UkLR6HRFgApwCTVfVoVf1f4BZgzYh7kqRF41AJi6XAE0PL21tNkjQPDht1A3MlyTpgXVt8Ickjo+zndeY44K9H3cRCkGvWjroFvZp/Pve5Ij/uHv72TCsOlbDYASwfWl7Waj9UVeuB9fPZ1GKRZKKqxkfdhzQd/3zOj0PlMtQ9wMokJyY5Ajgf2DTiniRp0Tgkziyqak+SS4HbgSXAhqp6cMRtSdKicUiEBUBVbQY2j7qPRcrLe1rI/PM5D1JVo+5BkrTAHSr3LCRJI2RY6IB8zYoWoiQbkuxK8sCoe1ksDAvNyNesaAG7EVg96iYWE8NCB+JrVrQgVdU3gN2j7mMxMSx0IL5mRRJgWEiSZsGw0IF0vmZF0uJgWOhAfM2KJMCw0AFU1R5g32tWHgZu9TUrWgiS3Ax8C/i7SbYnuXjUPb3e+QluSVInzywkSZ0MC0lSJ8NCktTJsJAkdTIsJEmdDAtpBJKs2PfG1CTjST7Z5k9P8guj7U56tUPmm/Kk16uqmgAm2uLpwAvA/xhZQ9I0PLOQDlKSf53kfyb5ZpKbk/zLJF9PMt7WH5fk8Ta/IslfJrm3Ta86a2hnE19JsgL4TeC3kmxL8otJHktyeBv3k8PL0nzyzEI6CEneyeC1J6sY/P25F9h6gE12Ae+pqpeSrARuBsanG1hVjyf5j8ALVXVNO97XgV8C/qwd90tV9f/m5JeRDoJnFtLB+UXgy1X1YlU9R/e7sg4HPpvkfuCPGXyJ1MH4T8BFbf4i4HMHub00JzyzkObGHl75z9cbh+q/BTwFvL2tf+lgdlpV/71dyjodWFJVfo2oRsIzC+ngfAM4N8mbkhwFvLfVHwfe2ebPGxr/ZmBnVf0A+ACwpGP/zwNH7Ve7CfgjPKvQCBkW0kGoqnuBLwLfAf6CwWvcAa4B/lmSbwPHDW3yGWBtku8AbwX+T8ch/hx4374b3K32BeAYBvc7pJHwrbPSjyHJlQzdkO7pGOcBa6rqA30dQ+riPQtpAUvyKeBs4JxR96LFzTMLSVIn71lIkjoZFpKkToaFJKmTYSFJ6mRYSJI6GRaSpE7/H6WR5BJvsqQcAAAAAElFTkSuQmCC\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ]
  },
  {
   "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 col in X.columns:\n",
    "    sns.boxplot(x=\"quality\", y=col,data=df)\n",
    "    plt.show()"
   ],
   "metadata": {
    "id": "OM_sE_Pxj64S",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 46,
   "outputs": [
    {
     "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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f/LlL0qPAZcDOes83M7M3ZrRZTB9I/gzgAHBl1b5g5CXANwPzJM2lEgzLqPQGRiVpBnAgIg5JOhf4PSqXuczMbJyMNovpYwCSisD1EfHLpD2DygJ+I51blnQd8BCVaa73RMR2SauA7ohYL+l3gH8BZgAfkHRrRLwdeBvwVUlHqVwG+/yQ2U9mZpaxepfaeMdgOABExMuSLhvtpIjYAGwYsu3mqvebqVx6GnreD4FL6qzNzBpIqVTi1ltv5ZZbbqFQKORdzpRW7yD1tKTXAICkc6g/XMzMxkyxWKSnp4e1a9fmXcqUV29A3AH8SNJnJX0W+CEeEzCzcVYqlejq6iIi6OrqolQq5V3SlFZXQETEWuCDwM+T1wcj4utZFmZmNlSxWOTo0cp9tQMDA+5FZKzeHgQR8UxE/G3y8oDxFNXU1DRi2yxPmzZtolwuA1Aul9m4cWPOFU1tdQeENYaIGLFtlqcrrrhixLaNLQeE1ZA0YtssT/7CMr4cEFZj3rx5Ne2LL744p0rMhnviiSdq2o8//nhOlTQGB4TV2LFjR037ueeey6kSs+EWLVp0rFcrifb29pwrmtocEFbDYxA2kXV2dh77nYwIli9fnnNFU5sDwswmjZdffnnEto0tB4SZTRqf+9znRmzb2HJAmNmk0dfXN2LbxpYDwswmjTlz5ozYtrHlgDCzSeOmm24asW1jywFhZpNGa2vrsV7DnDlzaG1tzbegKc4BYWaTyk033cQZZ5zh3sM48DMdrMb06dM5cuRITdtsImltbeU73/lO3mU0BPcgrEZ1OKS1zaxxOCDMzCyVA8LMzFJlGhCSOiTtkNQr6caU/e+WtFVSWdKHh+zrlPR88urMsk47btq0aSO2zaxxZPZ/v6Qm4C5gMTAfuEbS/CGHvQB8FLh3yLnnALcA7wIWALdImpFVrXbc4OMcT9Q2s8aR5dfDBUBvROyKiMPAOmBp9QER0RcR24Chfwu9H9gYEfsj4mVgI9CRYa1mZjZElgExC9hd1d6TbMv6XHsDzjrrrJr22WefnU8hZpa7SX2BWdIKSd2Suvft25d3OVPCK6+8UtP+5S9/mU8hZpa7LAOiHzi/qj072TZm50bE3RHRFhFtLS0tr7tQM5s8SqUSK1eupFQq5V3KlJdlQGwG5kmaK+kUYBmwvs5zHwKulDQjGZy+MtlmZg2uWCzS09PD2rVr8y5lysssICKiDFxH5S/2Z4H7ImK7pFWSlgBI+h1Je4A/BL4qaXty7n7gs1RCZjOwKtlmZg2sVCrR1dVFRNDV1eVeRMYyXYspIjYAG4Zsu7nq/WYql4/Szr0HuCfL+sxscikWi8emXg8MDLB27VpuuOGGnKuauib1ILWZNZZNmzZRLpcBKJfLbNy4MeeKpjYHhJlNGosWLaK5uXLho7m5mfb29pwrmtocEGY2aXR2dh5b/mXatGksX74854qmNgeEmU0ahUKBmTNnAjBz5kwKhULOFU1tDggzmzRKpRL9/ZVbol588UXPYsqYA8LMJo1isUhEAJWFJH0vRLYcEGY2aXgW0/hyQJjZpOFZTOPLAWFmk0b1LKampibPYsqYA8LMJo1CocB73/teABYuXOhZTBnLdKkNO3lf+tKX6O3tzbuMGtdff31uP7u1tZVPfepTuf18m3hefPFFAPbu3ZtzJVOfexBmNmmUSiV6enoA2LZtm6e5Zsw9iAkm72/LK1euZNu2bcfal19+OXfeeWeOFZkdt3r16pr2bbfdxh133JFTNVOfexBWY82aNTVth4NNJFu3bq1pb9myJadKGoMDwoY5/fTTgUrvwcwaly8x2TAXX3wx4N6D1ZqIEyggv0kUjTCBwj0IM5s0JI3YtrHlHoSZ1WUifFu+8847Wb/++KPtlyxZ4ifKZcg9CDObNDo7O4+9b25u9p3UGXNAmNmkUSgUjt09fdVVV/lO6oz5EpOZTSrnnXceBw8edO9hHGTag5DUIWmHpF5JN6bsP1XSN5P9/yZpTrJ9jqTfSHoqeX0lyzrNbPKYPn06ra2t7j2Mg8x6EJKagLuAdmAPsFnS+oh4puqwjwMvR0SrpGXAXwL/Ldm3MyIuzaq+oSbqFL48DP57yHMNpomkEaYzmqXJ8hLTAqA3InYBSFoHLAWqA2Ip8BfJ+/uBv1VO89Z6e3t56ifPMvCmc/L48RPKtMOVJ3Zt2fXznCvJX9OB/XmXYJabLANiFrC7qr0HeNeJjomIsqRXgMF+41xJTwKvAjdFxONDf4CkFcAKgAsuuOANFzzwpnP4zW///hv+HJs6Tn9uQ94lmOVmos5i2gtcEBGXAZ8G7pV05tCDIuLuiGiLiLaWlpZxL9LMbCrLsgfRD5xf1Z6dbEs7Zo+kZuAsoBSVp5IfAoiILZJ2AhcD3ZkV299P04FX/I3RajQdKNHfX867DI+RVfEYWa0sx8iyDIjNwDxJc6kEwTLgj4Ycsx7oBH4EfBh4OCJCUguwPyIGJL0VmAfsyrBWswmtt7eX57c/yQVvHsi7lNydcqRy4ePQzzL7vjhpvPBaU6afn1lAJGMK1wEPAU3APRGxXdIqoDsi1gN/D3xdUi+wn0qIALwbWCXpCHAUuDYiMh0tnDVrFv/vULPHIKzG6c9tYNas8/IuA4AL3jzA/7r81bzLsAnktq3DrryPqUxvlIuIDcCGIdturnp/EPjDlPMeAB7IsjYzMxuZ76Su0nRgv8cggGkHK99Sj56W7beTyaAyzTX/HkR/fz+//lVT5t8YbXL52a+aOKN/6NDu2HFAJFpbW/MuYcLo7f0VAK1vzf8vxvyd598Na1gOiITvlD1ucHbIF7/4xZwrsUGzZs3iUHmvxyCsxm1bz+TUWbMy+/yJeh+EmZnlzD0Is0nihdc8BgHw8wOV77XnvelozpXk74XXmpiX4ec7IMwmAY+DHHc4uVHu1Av972Qe2f5uOCDMJgGPkR3nMbLx4zEIMzNL5YAwM7NUDggzM0vlgLBh9u/fz9NPP80jjzySdylmliMHhA2ze3flOU+rV6/OuRIzy5MDwmo8/PDDx96Xy2X3IswamKe5TjB5Pxjm6aefrmnfeuutPPjgg/kUQ7YPQzGzkbkHYWZmqVR5uufk19bWFt3dfsLUG7Vw4cJh2x599NFxr8Mmnrx7t4MGa8j77vKp0ruVtCUi2tL2+RKT1ZBE9ZcGSTlWYzbc6aefnncJDcMBYTVmz559bBbTYNsMvNxHI/IYhNV46aWXRmybWeNwQFiN9vb2Y5eVJHHllVfmXJGZ5SXTgJDUIWmHpF5JN6bsP1XSN5P9/yZpTtW+P0+275D0/izrtOM6Oztpbq5ceZw+fTrLly/PuSIzy0tmASGpCbgLWAzMB66RNH/IYR8HXo6IVuCvgb9Mzp0PLAPeDnQAX04+zzJWKBRYvHgxkli8eDGFQiHvkswsJ1n2IBYAvRGxKyIOA+uApUOOWQoUk/f3A+9T5frGUmBdRByKiJ8Cvcnn2Tjo7Ozkkksuce/BrMFlGRCzgN1V7T3JttRjIqIMvAIU6jwXSSskdUvq3rdv3xiW3tgKhQJr1qxx78GswU3qQeqIuDsi2iKiraWlJe9yzMymlCwDoh84v6o9O9mWeoykZuAsoFTnuWZmlqEsA2IzME/SXEmnUBl0Xj/kmPVAZ/L+w8DDUbmNdz2wLJnlNJfKs7n/PcNazcxsiMzupI6IsqTrgIeAJuCeiNguaRXQHRHrgb8Hvi6pF9hPJURIjrsPeAYoA5+MiIGsajUzs+GmzGJ9kvYBP8u7jinkXMC3UdtE5d/PsXNhRKQO4k6ZgLCxJan7RCs8muXNv5/jY1LPYjIzs+w4IMzMLJUDwk7k7rwLMBuBfz/HgccgzMwslXsQZmaWygFhZmapHBA2zGjP8TDLg6R7JP1C0k/yrqVROCCsRp3P8TDLwz9SeT6MjRMHhA1Vz3M8zMZdRDxGZUkeGycOCBuqrmdxmNnU54AwM7NUDggbys/iMDPAAWHD1fMcDzNrAA4Iq5E8G3zwOR7PAvdFxPZ8qzIDSd8AfgT8lqQ9kj6ed01TnZfaMDOzVO5BmJlZKgeEmZmlckCYmVkqB4SZmaVyQJiZWSoHhNk4kTRncCVSSW2S1iTvF0r63XyrMxuuOe8CzBpRRHQD3UlzIfAa8MPcCjJL4R6EWR0kfUbSf0h6QtI3JP2ppEcltSX7z5XUl7yfI+lxSVuT17DeQdJr+FdJc4BrgRskPSXpCkk/lTQ9Oe7M6rbZeHIPwmwUkt5JZcmRS6n8P7MV2DLCKb8A2iPioKR5wDeAtrQDI6JP0leA1yLir5Kf9yhwFfBg8nP/OSKOjMk/jNlJcA/CbHRXAP8SEQci4lVGX5tqOvB3knqAb1F58NLJ+BrwseT9x4B/OMnzzcaEexBmr1+Z41+yTqvafgPwc+A/JfsPnsyHRsQPkstUC4GmiPAjNi0X7kGYje4x4GpJp0t6C/CBZHsf8M7k/Yerjj8L2BsRR4E/AZpG+fxfAW8Zsm0tcC/uPViOHBBmo4iIrcA3gaeB71JZEh3gr4BPSHoSOLfqlC8DnZKeBn4b+PUoP+LbwH8ZHKROtv0TMIPK+IVZLryaq9lJkvQXVA0qZ/QzPgwsjYg/yepnmI3GYxBmE4ykLwGLgd/PuxZrbO5BmJlZKo9BmJlZKgeEmZmlckCYmVkqB4SZmaVyQJiZWar/D17jUS0NJBUyAAAAAElFTkSuQmCC\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"
    }
   ]
  },
  {
   "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 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",
    "mod = sm.Logit(y,X)\n",
    "\n",
    "res = mod.fit()\n",
    "\n",
    "print(res.summary())"
   ],
   "metadata": {
    "id": "6jZW_2WrRtsu",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 51,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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:                        16:46:03   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",
      "Intercept    -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"
     ]
    }
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "**5) Refit the same model as above, but introduce an interaction term between the variables 'density' and 'alcohol'.**\n",
    "\n",
    "**What do you observe ? 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",
    "mod = sm.Logit(y,X)\n",
    "\n",
    "res = mod.fit()\n",
    "\n",
    "print(res.summary())"
   ],
   "metadata": {
    "id": "LN6B0eigOkZI",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 52,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "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:                        16:47:24   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": [
    "# 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 the 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, and this boundary decision. 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": [],
   "metadata": {
    "id": "N9cD5dR3HyOt",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 52,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "source": [
    "**7) Select th 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": [],
   "metadata": {
    "id": "6ToaKHeQa_hZ",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 52,
   "outputs": []
  },
  {
   "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','chlorides']]\n",
    "y = df['quality']\n",
    "\n",
    "models = [LogisticRegression(solver=\"liblinear\"), LinearDiscriminantAnalysis(),\n",
    "          QuadraticDiscriminantAnalysis(), GaussianNB()]\n",
    "\n",
    "for model in models:\n",
    "    print(model)\n",
    "    cv_results = cross_validate(model, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
    "\n",
    "    train_acc = cv_results['train_accuracy']\n",
    "    test_acc = cv_results['test_accuracy']\n",
    "\n",
    "    mean_train_acc = train_acc.mean()\n",
    "    mean_test_acc = test_acc.mean()\n",
    "\n",
    "    print('Train accuracy : {}'.format(mean_train_acc))\n",
    "    print('Test accuracy : {}'.format(mean_test_acc))\n",
    "    print()\n"
   ],
   "metadata": {
    "id": "ZTPecde9HjyV",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 55,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression(solver='liblinear')\n",
      "Train accuracy : 0.8009619204078113\n",
      "Test accuracy : 0.7964429698259672\n",
      "\n",
      "LinearDiscriminantAnalysis()\n",
      "Train accuracy : 0.7967651240512416\n",
      "Test accuracy : 0.7923525729310128\n",
      "\n",
      "QuadraticDiscriminantAnalysis()\n",
      "Train accuracy : 0.779501809942458\n",
      "Test accuracy : 0.775400025040691\n",
      "\n",
      "GaussianNB()\n",
      "Train accuracy : 0.7609906358014603\n",
      "Test accuracy : 0.7578298067693335\n",
      "\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",
    "models = [LogisticRegression(solver=\"liblinear\"), LinearDiscriminantAnalysis(),\n",
    "          QuadraticDiscriminantAnalysis(), GaussianNB()]\n",
    "\n",
    "for model in models:\n",
    "    print(model)\n",
    "    cv_results = cross_validate(model, X, y, cv=10, scoring=['accuracy'], return_train_score=True)\n",
    "\n",
    "    train_acc = cv_results['train_accuracy']\n",
    "    test_acc = cv_results['test_accuracy']\n",
    "\n",
    "    mean_train_acc = train_acc.mean()\n",
    "    mean_test_acc = test_acc.mean()\n",
    "\n",
    "    print('Train accuracy : {}'.format(mean_train_acc))\n",
    "    print('Test accuracy : {}'.format(mean_test_acc))\n",
    "    print()"
   ],
   "metadata": {
    "id": "1wUctrK4rSdg",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 56,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression(solver='liblinear')\n",
      "Train accuracy : 0.8017557100453248\n",
      "Test accuracy : 0.7962351320896457\n",
      "\n",
      "LinearDiscriminantAnalysis()\n",
      "Train accuracy : 0.8024362496444535\n",
      "Test accuracy : 0.7964346229289261\n",
      "\n",
      "QuadraticDiscriminantAnalysis()\n",
      "Train accuracy : 0.7547070029583935\n",
      "Test accuracy : 0.7394628771754099\n",
      "\n",
      "GaussianNB()\n",
      "Train accuracy : 0.727984074194057\n",
      "Test accuracy : 0.7261821292934352\n",
      "\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": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\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",
   "execution_count": 52,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ]
}