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for t in tqdm(range(1, T + 1), desc="Boosting Iterations"):
    # Step 3.1: Train decision stump
    feature, theta, s, epsilon = train_decision_stump(X_train, y_train, u)
    stump_info.append((feature, theta, s))
    
    # Step 3.2: Calculate alpha
    # alpha = log(sqrt((1 - epsilon) / epsilon)) = log((1 - epsilon) / epsilon)) / 2
    alpha = np.log((1 - epsilon) / max(epsilon, 1e-10)) / 2
    alpha_values.append(alpha)
    
    # Step 3.3: Update weights
    predictions = s * np.sign(X_train[:, feature] - theta)
    u = u * np.exp(-alpha * y_train * predictions)
    U_t.append(np.sum(u))

    # Store metrics
    Ein_gt.append(np.mean(predictions != y_train))
    epsilon_t.append(epsilon)

    # Step 3.4: Update combined hypothesis G_t
    G_t += alpha * predictions
    G_train_predictions = np.sign(G_t)
    Ein_Gt.append(np.mean(G_train_predictions != y_train))

    G_test += alpha * (s * np.sign(X_test[:, feature] - theta))
    G_test_predictions = np.sign(G_test)
    Eout_Gt.append(np.mean(G_test_predictions != y_test))