First exercise

.gitignore

@@ -1 +1,2 @@
 .DS_Store
+.vscode/*

cours_ex1.py

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+import random
+import numpy as np
+from numpy import arange
+import matplotlib.pyplot as plt
+
+random.seed(0)
+
+def line_w_gauss_noise(inter,slope,noise,numPoints):
+    x = np.zeros(shape=(numPoints, 2))
+    y = np.zeros(shape=numPoints)
+    for i in range(0, numPoints):
+        x[i][0] = i
+        x[i][1] = 1
+        y[i] = (i + inter) + random.uniform(0, noise) * slope
+    return x, y
+
+
+def MSE(x,y,weights):
+    N,D = np.shape(x)
+    x_T = x.transpose()
+    y_hat = np.dot(weights,x_T)
+    return np.sum((y - y_hat)**2) / N
+
+
+def dMSE(x,y,weights):
+    N = len(x)
+    inter = np.sum(np.dot(np.dot(x[:,1],weights[1]) - y,x[:,1])) * (2/N)
+    slope = np.sum(np.dot(x[:,0],weights[0]) - y,) * (2/N)
+    new_weight = np.array([slope,inter])
+    return new_weight
+
+def gradient_desscent(x,y,alpha,weights,iter):
+    losses = list()
+    costs = list()
+    for n in range(iter):
+        cost = MSE(x,y,weights)
+        loss = np.sum(y - np.dot(x,weights))
+        losses.append(loss)
+        costs.append(cost)
+        print(cost)
+        print(loss)
+        print(n)
+        if np.abs(losses[n]) > np.abs(losses[n-1]):
+            break
+
+        weights = weights - (alpha * dMSE(x,y,weights))
+    return weights,costs,losses
+
+if __name__ == '__main__':
+    x,y = line_w_gauss_noise(1,2,5,100)
+    num_var = len(x.transpose())
+    w = np.ones(num_var)
+
+    result,cost,loss = gradient_desscent(x,y,0.001,w,80)
+    print(result)
+    y_hat = []
+    for i in x[:,0]:
+        y_hat.append(result[1]+(result[0]*i))
+
+    plt.scatter(x[:,0],y)
+    plt.plot(x[:,0],y_hat)
+    plt.show()
+
+    #plt.plot(cost)
+    #plt.plot(loss)
+    #plt.show()