Implemented task 3 and 4

effect-of-regularization-on-loss.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+# Generating Synthetic Data
+def generate_linear_data(n):
+    x = np.random.uniform(0, 10, n) # initialize x
+    eps = np.random.normal(0, 1, n) # initialize epsilon
+    y = -3 * x + 8 + 2 * eps # y = −3x + 8 + 2ϵ
+    return x.reshape(-1, 1), y
+
+# Gradient Descent with L1/L2
+def gradient_descent(x, y, lam, reg_type, lr, iters):
+    x_b = np.hstack([np.ones_like(x), x]) # initialize x
+    w = np.zeros(x_b.shape[1]) # initialize weight
+    path = [w.copy()]
+
+    for i in range(iters):
+        pred = x_b @ w # linear regression prediction
+        error = pred - y # error
+        grad = x_b.T @ error / len(y) # gradient formula
+
+        if reg_type == 'l2':
+            grad += lam * w # L2 formula
+        elif reg_type == 'l1':
+            grad += lam * np.sign(w) # L1 formula
+
+        w -= lr * grad # loss calculation
+        path.append(w.copy())
+
+    return w, np.array(path)
+
+# Plotting the loss
+def plot_contour(x, y, reg_type, lam):
+    x_b = np.hstack([np.ones_like(x), x]) # initialize x
+    w0, w1 = np.meshgrid(np.linspace(-10, 10, 100), np.linspace(-10, 10, 100)) # initialize intercept and slope
+    loss = np.zeros_like(w0) # initialize loss
+
+    for i in range(w0.shape[0]):
+        for j in range(w0.shape[1]):
+            w = np.array([w0[i, j], w1[i, j]])
+            error = y - x_b @ w # error
+            mse = np.mean(error ** 2) # mean square error
+            reg = lam * (np.sum(w ** 2) if reg_type == 'l2' else np.sum(np.abs(w))) # regularization
+            loss[i, j] = mse + reg # regularization and mse for the loss
+
+    _, path = gradient_descent(x, y, lam, reg_type, 0.01, 500)
+
+    # plotting the figure
+    plt.figure(figsize=(6, 5))
+    plt.contour(w0, w1, loss, levels=50, cmap='viridis')
+    plt.plot(path[:, 0], path[:, 1], 'ro-', markersize=2, label='Gradient Descent Path')
+    plt.title(f"{reg_type.upper()} Regularization (λ={lam})")
+    plt.xlabel("w0 (intercept)")
+    plt.ylabel("w1 (slope)")
+    plt.grid(True)
+    plt.legend()
+    plt.tight_layout()
+    plt.savefig('results/task4-effect-of-regularization-on-loss-' + reg_type + '-'  + str(lam) + '.png')
+
+if __name__ == "__main__":
+    print("Running Task 4: Effect of L1 and L2 Regularization on Loss Landscape")
+
+    # Generate dataset
+    x, y = generate_linear_data(30)
+
+    # Values of lambda to visualize
+    lambda_values = [0.01, 0.1, 1.0]
+
+    # Plot for both L1 and L2 regularization
+    for reg_type in ['l1', 'l2']:
+        for lam in lambda_values:
+            plot_contour(x, y, reg_type, lam)