From adf935d62abcef3ce57c201c76776d374ae61ee8 Mon Sep 17 00:00:00 2001
From: Emmanuel Dellandrea <emmanuel.dellandrea@ec-lyon.fr>
Date: Fri, 10 Jan 2025 08:42:08 +0100
Subject: [PATCH] MAJ regression logistique

---
 Cours/ML-04-Regression_logistique.pdf | Bin 753718 -> 771139 bytes
 TD/TD3/ML-TD3.pdf                     | Bin 0 -> 73999 bytes
 TD/TD3/notes.txt                      | 100 ++++++++++
 TD/TD3/regression_logistique.py       | 262 ++++++++++++++++++++++++++
 4 files changed, 362 insertions(+)
 create mode 100644 TD/TD3/ML-TD3.pdf
 create mode 100644 TD/TD3/notes.txt
 create mode 100644 TD/TD3/regression_logistique.py

diff --git a/Cours/ML-04-Regression_logistique.pdf b/Cours/ML-04-Regression_logistique.pdf
index 60d80d5d7aaa828460e4bd16f0d3b60fb44b9a31..38c59b03cefd66e98648791f8a924f0c12ceaab6 100644
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diff --git a/TD/TD3/notes.txt b/TD/TD3/notes.txt
new file mode 100644
index 0000000..3a5f952
--- /dev/null
+++ b/TD/TD3/notes.txt
@@ -0,0 +1,100 @@
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diff --git a/TD/TD3/regression_logistique.py b/TD/TD3/regression_logistique.py
new file mode 100644
index 0000000..71448b1
--- /dev/null
+++ b/TD/TD3/regression_logistique.py
@@ -0,0 +1,262 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+def lecture_donnees(nom_fichier, delimiteur=','):
+    """ Lit le fichier contenant les données et renvoiee les matrices correspondant
+
+    Parametres
+    ----------
+    nom_fichier : nom du fichier contenant les données
+    delimiteur : caratère délimitant les colonne dans le fichier ("," par défaut)
+
+    Retour
+    -------
+    X : matrice des données de dimension [N, nb_var]
+    Y : matrice contenant les valeurs de la variable cible de dimension [N, 1]
+    N : nombre d'éléments
+    nb_var : nombre de variables prédictives
+
+    """
+    
+    data = np.loadtxt(nom_fichier, delimiter=delimiteur)
+
+    #######################
+    ##### A compléter ##### 
+    #######################
+    
+    # return X, Y, N, nb_var
+
+def normalisation(X):
+    """ Normalise les données par un centrage-réduction des variables prédictives
+    
+    Parametres
+    ----------
+    X : matrice des données de dimension [N, nb_var]
+    
+    avec N : nombre d'éléments et nb_var : nombre de variables prédictives
+
+    Retour
+    -------
+    X_norm : matrice des données centrées-réduites de dimension [N, nb_var]
+    mu : moyenne des variables de dimension [1,nb_var]
+    sigma : écart-type des variables de dimension [1,nb_var]
+    
+    """
+    
+    #########################################################
+    ##### A compléter (et supprimer l'instruction pass) ##### 
+    #########################################################
+    pass
+
+    # return X_norm, mu, sigma
+
+def sigmoide(z):
+    """ Calcule la valeur de la fonction sigmoide appliquée à z
+    
+    Parametres
+    ----------
+    z : peut être un scalaire ou une matrice
+
+    Return
+    -------
+    s : valeur de sigmoide de z. Même dimension que z
+
+    """
+
+    #########################################################
+    ##### A compléter (et supprimer l'instruction pass) ##### 
+    #########################################################
+    pass
+
+    # return s
+
+def calcule_cout(X, Y, theta):
+    """ Calcule la valeur de la fonction cout ( - log vraisemblance)
+    
+    Parametres
+    ----------
+    X : matrice des données de dimension [N, nb_var+1]
+    Y : matrice contenant les valeurs de la variable cible de dimension [N, 1]
+    theta : matrices contenant les paramètres theta du modèle linéaire de dimension [1, nb_var+1]
+    
+    avec N : nombre d'éléments et nb_var : nombre de variables prédictives
+
+    Return
+    -------
+    cout : nombre correspondant à la valeur de la fonction cout (moyenne des différences au carré)
+
+    """
+
+    #########################################################
+    ##### A compléter (et supprimer l'instruction pass) ##### 
+    #########################################################
+    pass
+
+    # return cout
+
+def descente_gradient(X, Y, theta, alpha, nb_iters):
+    """ Apprentissage des parametres de regression linéaire par descente du gradient
+    
+    Parametres
+    ----------
+    X : matrice des données de dimension [N, nb_var+1]
+    Y : matrice contenant les valeurs de la variable cible de dimension [N, 1]
+    theta : matrices contenant les paramètres theta du modèle linéaire de dimension [1, nb_var+1]
+    alpha : taux d'apprentissage
+    nb_iters : nombre d'itérations
+    
+    avec N : nombre d'éléments et nb_var : nombre de variables prédictives
+
+
+    Retour
+    -------
+    theta : matrices contenant les paramètres theta appris par descente du gradient de dimension [1, nb_var+1]
+    J_history : tableau contenant les valeurs de la fonction cout pour chaque iteration de dimension nb_iters
+
+
+    """
+    
+    # Initialisation de variables utiles
+    N = X.shape[0]
+    J_history = np.zeros(nb_iters)
+
+    #########################################################
+    ##### A compléter (et supprimer l'instruction pass) ##### 
+    #########################################################
+    pass
+        
+
+    return theta, J_history
+
+def prediction(X,theta):
+    """ Predit la classe de chaque élement de X
+    
+    Parametres
+    ----------
+    X : matrice des données de dimension [N, nb_var+1]
+    theta : matrices contenant les paramètres theta du modèle linéaire de dimension [1, nb_var+1]
+    
+    avec N : nombre d'éléments et nb_var : nombre de variables prédictives
+
+
+    Retour
+    -------
+    p : matrices de dimension [N,1] indiquant la classe de chaque élement de X (soit 0, soit 1)
+
+    """
+
+    #########################################################
+    ##### A compléter (et supprimer l'instruction pass) ##### 
+    #########################################################
+    pass
+
+    # return p
+
+def taux_classification(Ypred,Y):
+    """ Calcule le taux de classification (proportion d'éléments bien classés)
+    
+    Parametres
+    ----------
+    Ypred : matrice contenant les valeurs de classe prédites de dimension [N, 1]
+    Y : matrice contenant les valeurs de la variable cible de dimension [N, 1]
+    
+    avec N : nombre d'éléments 
+
+
+    Retour
+    -------
+    t : taux de classification
+
+    """
+
+    #########################################################
+    ##### A compléter (et supprimer l'instruction pass) ##### 
+    #########################################################
+    pass
+
+    # return t
+
+def affichage(X, Y):
+    """ Affichage en 2 dimensions des données (2 dimensions de X) et représentation de la 
+        classe (indiquée par Y) par une couleur
+    
+
+    Parametres
+    ----------
+    X : matrice des données de dimension [N, nb_var+1]
+    Y : matrice contenant les valeurs de la variable cible de dimension [N, 1]
+    
+    avec N : nombre d'éléments et nb_var : nombre de variables prédictives
+
+    Retour
+    -------
+    None
+
+    """
+
+    #########################################################
+    ##### A compléter (et supprimer l'instruction pass) ##### 
+    #########################################################
+    pass
+
+
+if __name__ == "__main__":
+    # ===================== Partie 1: Lecture et normalisation des données=====================
+    print("Lecture des données ...")
+
+    X, Y, N, nb_var = lecture_donnees("notes.txt")
+
+    # Affichage des 10 premiers exemples du dataset
+    print("Affichage des 10 premiers exemples du dataset : ")
+    for i in range(0, 10):
+        print(f"x = {X[i,:]}, y = {Y[i]}")
+        
+    # Normalisation des variables (centrage-réduction)
+    print("Normalisation des variables ...")
+
+    X, mu, sigma = normalisation(X)
+
+    # Ajout d'une colonne de 1 à X (pour theta0)
+    X = np.hstack((np.ones((N,1)), X)) 
+
+    # Affichage des points en 2D et représentation de leur classe réelle par une couleur
+    if nb_var == 2 :
+        plt.figure(0)
+        plt.title("Disposition des points en 2D - Réalité")
+        affichage(X,Y)
+
+    # ===================== Partie 2: Descente du gradient =====================
+    print("Apprentissage par descente du gradient ...")
+
+    # Choix du taux d'apprentissage et du nombre d'itérations
+    alpha = 0.01
+    nb_iters = 10000
+
+    # Initialisation de theta et réalisation de la descente du gradient
+    theta = np.zeros((1,nb_var+1))
+    theta, J_history = descente_gradient(X, Y, theta, alpha, nb_iters)
+
+    # Affichage de l'évolution de la fonction de cout lors de la descente du gradient
+    plt.figure(1)
+    plt.title("Evolution de le fonction de cout lors de la descente du gradient")
+    plt.plot(np.arange(J_history.size), J_history)
+    plt.xlabel("Nombre d'iterations")
+    plt.ylabel("Cout J")
+
+    # Affichage de la valeur de theta
+    print(f"Theta calculé par la descente du gradient : {theta}")
+
+    # Evaluation du modèle
+    Ypred = prediction(X,theta)
+
+    print("Taux de classification : ", taux_classification(Ypred,Y))
+
+    # Affichage des points en 2D et représentation de leur classe prédite par une couleur
+    if nb_var == 2 :
+        plt.figure(2)
+        plt.title("Disposition des points en 2D - Prédiction")
+        affichage(X,Ypred)
+        
+    plt.show()
+
+    print("Regression logistique Terminée.")
-- 
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