Régression Linéaire Multiple

1. Génération des données

# Génération de 100 points, 2 variables
import numpy as np
from sklearn.datasets import make_regression
x, y = make_regression(n_samples=100, n_features=2, noise=10)

y = y.reshape(y.shape[0], 1)
# Génération de la matrice X
X = np.hstack((x, np.ones((x.shape[0], 1)))) 
    

2. Modèle, coût, descente de gradient

def modele(X, theta):
    return X.dot(theta)

def cost_function(X, y, theta):
    m = len(y)
    return 1/(2*m)*np.sum((modele(X, theta)-y)**2)

def grad(X, y, theta):
    m = len(y)
    return 1/m*X.T.dot(modele(X, theta)-y)

def gradient_descent(X, y, theta, learning_rate, n_iterations):
    cost_history = np.zeros(n_iterations)
    for i in range(n_iterations):
        theta = theta - learning_rate * grad(X, y, theta)
        cost_history[i] = cost_function(X, y, theta)
    return theta, cost_history

theta = np.random.randn(3,1)
theta_final, cost_history = gradient_descent(X, y, theta, 0.01, 1000)
    

3. Visualisation 3D interactive

4. Évaluation du modèle

def coef_determination(y, pred):
    u = ((y - pred)**2).sum()
    v = ((y - y.mean())**2).sum()
    return 1-u/v

print(coef_determination(y, predictions))