finished chapter 5

05_01_gradient.py

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+import numpy as np
+
+# linear regression, no bias
+# f = w*x
+# f = 2*x
+
+X = np.array([1, 2, 3, 4], dtype=np.float32)
+Y = np.array([2, 4, 6, 8], dtype=np.float32)
+
+w = 0.0
+
+# model prediction
+def forward(x):
+    return w*x
+
+# loss = MSE
+def loss(y, y_pred):
+    return ((y_pred - y)**2).mean()
+
+# gradient
+# mse = 1/N * (w*x - y)**2
+# dJ/dw = 1/N * 2x * (w*x - y)
+def gradient(x, y, y_pred):
+    return np.dot(2*x, y_pred-y).mean()
+
+print(f'Prediction before training: f(5) = {forward(5):.3f}')
+
+#Training
+learning_rate = .01
+n_iters = 20
+
+for epoch in range(n_iters):
+    # prediction = forward pass
+    y_pred = forward(X)
+
+    # loss
+    l = loss(Y, y_pred)
+
+    # gradients
+    dw = gradient(X, Y, y_pred)
+
+    #update weights
+    w -= learning_rate*dw
+
+    if epoch % 2 == 0: #every nth epoch
+        print(f'epoch {epoch+1}: w = {w:.3f}, loss = {l:.8f}')
+
+print(f'Prediction after training: f(5) = {forward(5):.3f}')