update

doc/src/week40/week40.do.txt

@@ -144,7 +144,7 @@ the number of minibatches, as exemplified in the code below.
 import numpy as np 
 
 n = 100 #100 datapoints 
-M = 5   #size of each minibatch
+M = 5   #size of each mini-batche
 m = int(n/M) #number of minibatches
 n_epochs = 10 #number of epochs
 
@@ -222,7 +222,7 @@ print("gamma_j after %d epochs: %g" % (n_epochs,gamma_j))
 !ec
 
 
-
+We note that we have defined several hyperparameters. These are now the number of epochs, the number of mini-batches and the parameters $t_0$ and $t_1$.
 
 
 !split
@@ -236,9 +236,9 @@ import numpy as np
 import matplotlib.pyplot as plt
 from sklearn.linear_model import SGDRegressor
 
-m = 100
-x = 2*np.random.rand(m,1)
-y = 4+3*x+np.random.randn(m,1)
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
 
 X = np.c_[np.ones((m,1)), x]
 theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)
@@ -256,7 +256,7 @@ Niterations = 1000
 
 
 for iter in range(Niterations):
-    gradients = 2.0/m*X.T @ ((X @ theta)-y)
+    gradients = 2.0/n*X.T @ ((X @ theta)-y)
     theta -= eta*gradients
 print("theta from own gd")
 print(theta)
@@ -268,7 +268,7 @@ ypredict2 = Xnew.dot(theta_linreg)
 
 
 n_epochs = 50
-M = 10   #size of each minibatch
+M = 5   #size of each minibatch
 m = int(n/M) #number of minibatches
 t0, t1 = 5, 50
 def learning_schedule(t):
@@ -281,7 +281,7 @@ for epoch in range(n_epochs):
         random_index = np.random.randint(m)
         xi = X[random_index:random_index+1]
         yi = y[random_index:random_index+1]
-        gradients = 2 * xi.T @ ((xi @ theta)-yi)
+        gradients = (2.0/m) * xi.T @ ((xi @ theta)-yi)
         eta = learning_schedule(epoch*m+i)
         theta = theta - eta*gradients
 print("theta from own sdg")