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# Mini-batch Gradient Descent | |
n_iterations = 50 | |
minibatch_size = 20 | |
m = 100 | |
X = 2 * np.random.rand(100, 1) | |
y = 4 + 3 * X + np.random.randn(100, 1) | |
X_b = np.c_[np.ones((100, 1)), X] # add x0 = 1 to each instance | |
np.random.seed(42) | |
theta = np.random.randn(2,1) # random initialization | |
t0, t1 = 200, 1000 | |
def learning_schedule(t): | |
return t0 / (t + t1) | |
t = 0 | |
for epoch in range(n_iterations): | |
shuffled_indices = np.random.permutation(m) | |
X_b_shuffled = X_b[shuffled_indices] | |
y_shuffled = y[shuffled_indices] | |
for i in range(0, m, minibatch_size): | |
t += 1 | |
xi = X_b_shuffled[i:i+minibatch_size] | |
yi = y_shuffled[i:i+minibatch_size] | |
gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi) | |
eta = learning_schedule(t) | |
theta = theta - eta * gradients | |
print(theta) |
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