{ "cells": [ { "cell_type": "markdown", "id": "3960a901", "metadata": {}, "source": [ "# Centre Universitaire de Mila" ] }, { "cell_type": "markdown", "id": "c4568d4a", "metadata": {}, "source": [ "## Master 1 (STIC & I2A), Matière: Apprentissage Automatique" ] }, { "cell_type": "markdown", "id": "a8bedc4a", "metadata": {}, "source": [ "## Travaux pratiques N°2 Apprentissage supervisé et régression" ] }, { "cell_type": "markdown", "id": "f57e8c63", "metadata": {}, "source": [ "## Exercice 1 :" ] }, { "attachments": { "img1.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "751221fd", "metadata": {}, "source": [ "En utilisant les formules de la régression linéaire et les fonctions Python de la bibliothèque Scikit-Learn:\n", "1) Générer les données aléatoires\n", "calculer le modèle de régression linéaire pour l’exemple suivant (vue en cours):\n", "\n", "![img1.png](attachment:img1.png)\n", "\n", "| x | y |\n", "| --- | --- |\n", "| 0.86 | 2.49 |\n", "| 0.09 | 0.83 |\n", "| -0.85 | -0.25 |\n", "| 0.87 | 3.10 |\n", "| -0.44 | 0.87 |\n", "| -0.43 | 0.02 |\n", "| -1.10 | -0.12 |\n", "| 0.40 | 1.81 |\n", "| -0.96 | -0.83 |\n", "| 0.17 | 0.43 |\n" ] }, { "cell_type": "markdown", "id": "11ae8da9", "metadata": {}, "source": [ "## Solution de l'exercice 1" ] }, { "cell_type": "markdown", "id": "aa55f351", "metadata": {}, "source": [ "### 1) Initialisation de l'environement Python:" ] }, { "cell_type": "code", "execution_count": 1, "id": "646ce80c-b0d2-45ab-9f81-b593c00b35b2", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "np.random.seed(42)\n", "def save_fig(name):\n", " plt.tight_layout()\n", " plt.savefig(name + \".png\", dpi=300)" ] }, { "cell_type": "markdown", "id": "2e700e39", "metadata": {}, "source": [ "### 2) Initialiser les variables des données:" ] }, { "cell_type": "code", "execution_count": 2, "id": "a8c9e7f7-acdf-47dd-b11f-5f1a532b76e4", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "X = np.array([[0.86], \n", " [0.09], \n", " [-0.85], \n", " [0.87], \n", " [-0.44], \n", " [-0.43], \n", " [-1.10], \n", " [0.40], \n", " [-0.96], \n", " [0.17]])\n", "\n", "y = np.array([2.49, \n", " 0.83, \n", " -0.25, \n", " 3.10, \n", " 0.87, \n", " 0.02, \n", " -0.12, \n", " 1.81, \n", " -0.83, \n", " 0.43])\n" ] }, { "cell_type": "markdown", "id": "5245571d", "metadata": {}, "source": [ "### 3) Afficher les données sur un plans 2D:" ] }, { "cell_type": "code", "execution_count": 3, "id": "556d6dcd", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X, y, \"b.\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.axis([-1.5, 2, -1.5, 4])\n", "save_fig(\"generated_data_plot\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a15364b8", "metadata": {}, "source": [ "### 4) Calculer les paramétres du modèle par la méthode des erreur des moindres carrés :" ] }, { "cell_type": "code", "execution_count": 4, "id": "087e0964-988f-4fd9-aa44-92a8aa159ce2", "metadata": {}, "outputs": [], "source": [ "X_b = np.c_[np.ones((X.shape[0], 1)), X] \n", "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y) " ] }, { "cell_type": "markdown", "id": "a38dac4a", "metadata": {}, "source": [ "### 5) Afficher les paramétres trouvés :" ] }, { "cell_type": "code", "execution_count": 5, "id": "a1f7545d-1f4b-44c1-b18e-c431f15b6715", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.05881341, 1.61016842])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta_best" ] }, { "cell_type": "markdown", "id": "aafed1cf", "metadata": {}, "source": [ "### 6) Calculer les valeurs predites pour les examples -1.5 et 2 :" ] }, { "cell_type": "code", "execution_count": 6, "id": "c324d4fe-2c1b-47ba-bde9-5e3ee91181cc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-1.35643922, 4.27915024])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_new = np.array([[-1.5], [2]])\n", "\n", "# Ajout d'une colonne de 1 pour le biais (intercept)\n", "X_new_b = np.c_[np.ones((X_new.shape[0], 1)), X_new] \n", "\n", "# Prédiction des valeurs de y avec le modèle de régression linéaire\n", "y_predict = X_new_b.dot(theta_best)\n", "\n", "# Affichage des prédictions\n", "y_predict" ] }, { "cell_type": "markdown", "id": "0d58aca5", "metadata": {}, "source": [ "### 7) Afficher les données d'apprentissage avec le modèle superimposés:" ] }, { "cell_type": "code", "execution_count": 8, "id": "c5ddcc1d", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(X_new, y_predict, \"r-\")\n", "plt.plot(X, y, \"b.\")\n", "plt.axis([-1.5, 2, -1.5, 4])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0f9b8669", "metadata": {}, "source": [ "## Exercice 2 :" ] }, { "attachments": { "img2.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "aef2d7eb", "metadata": {}, "source": [ "Même question que l’exercice 1, avec le 2ieme exemple qui illustre une régression quadratique (m = 2) :\n", "\n", "![img2.png](attachment:img2.png)" ] }, { "cell_type": "markdown", "id": "7a719372", "metadata": {}, "source": [ "## Solution de l'exercice 2" ] }, { "cell_type": "markdown", "id": "7bfeb39b", "metadata": {}, "source": [ "### 1) Initialiser les variables des données:" ] }, { "cell_type": "code", "execution_count": 13, "id": "cccbefc8-3269-47d1-a2aa-18054cae7786", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X=\n", "[[ 0.86]\n", " [ 0.09]\n", " [-0.85]\n", " [ 0.87]\n", " [-0.44]\n", " [-0.43]\n", " [-1.1 ]\n", " [ 0.4 ]\n", " [-0.96]\n", " [ 0.17]]\n", "y=\n", "[[ 2.49]\n", " [ 0.83]\n", " [-0.25]\n", " [ 3.1 ]\n", " [ 0.87]\n", " [ 0.02]\n", " [-0.12]\n", " [ 1.81]\n", " [-0.83]\n", " [ 0.43]]\n" ] } ], "source": [ "X = np.array([[0.86], [0.09], [-0.85], [0.87], [-0.44], [-0.43], [-1.1], [0.4], [-0.96], [0.17]])\n", "y = np.array([[2.49], [0.83], [-0.25], [3.1], [0.87], [0.02], [-0.12], [1.81], [-0.83], [0.43]])\n", "print('X=')\n", "print(X)\n", "print('y=')\n", "print(y)" ] }, { "cell_type": "markdown", "id": "68e9ae74", "metadata": {}, "source": [ "### 2) Calculer les paramétres du modèle par la méthode des erreur des moindres carrés :" ] }, { "cell_type": "code", "execution_count": 10, "id": "2e28fe80", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.86])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n", "X_poly = poly_features.fit_transform(X)\n", "X[0]" ] }, { "cell_type": "code", "execution_count": 13, "id": "4a42ed50", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.86 , 0.7396],\n", " [ 0.09 , 0.0081],\n", " [-0.85 , 0.7225],\n", " [ 0.87 , 0.7569],\n", " [-0.44 , 0.1936],\n", " [-0.43 , 0.1849],\n", " [-1.1 , 1.21 ],\n", " [ 0.4 , 0.16 ],\n", " [-0.96 , 0.9216],\n", " [ 0.17 , 0.0289]])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_poly[:]" ] }, { "cell_type": "code", "execution_count": 11, "id": "2d95613e-c24c-41dd-a6c9-fd2deaeca9ab", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7396088751138912, array([1.74736998, 0.68670054]))" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.linear_model import LinearRegression\n", "lin_reg = LinearRegression()\n", "lin_reg.fit(X_poly, y)\n", "lin_reg.intercept_, lin_reg.coef_" ] }, { "cell_type": "markdown", "id": "deadbea8", "metadata": {}, "source": [ "### 3) Afficher les données d'apprentissage avec le modèle superimposés:" ] }, { "cell_type": "code", "execution_count": 83, "id": "e5344c4d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Saving figure quadratic_predictions_plot\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n", "X_new_poly = poly_features.transform(X_new)\n", "y_new = lin_reg.predict(X_new_poly)\n", "plt.plot(X, y, \"b.\")\n", "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n", "plt.xlabel(\"$x_1$\", fontsize=18)\n", "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", "plt.legend(loc=\"upper left\", fontsize=14)\n", "plt.axis([-1.5, 2, -1.5, 4])\n", "save_fig(\"quadratic_predictions_plot\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "df0aa53f", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 5 }