CART决策树之回归用法

from sklearn.tree import DecisionTreeRegressor

import numpy as np
import matplotlib.pyplot as plt
from sklearn.tree import DecisionTreeRegressor

# 1. 构建CART回归树示例
def cart_regression_demo():
    """CART回归树示例"""
    # 示例数据
    X = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]).reshape(-1, 1)
    y = np.array([5.56, 5.70, 5.91, 6.40, 6.80, 7.05, 8.90, 8.70, 9.00, 9.05])
    
    print("=== 原始数据 ===")
    print(f"X: {X.ravel()}")
    print(f"y: {y}")
    
    # 2. 手动计算平方损失
    print("\n=== 手动计算平方损失 ===")
    
    def calculate_loss(X, y, split_point):
        """计算在指定切分点的平方损失"""
        left_mask = X.ravel() <= split_point
        right_mask = X.ravel() > split_point
        
        left_y = y[left_mask]
        right_y = y[right_mask]
        
        # 预测值 = 均值
        left_pred = left_y.mean() if len(left_y) > 0 else 0
        right_pred = right_y.mean() if len(right_y) > 0 else 0
        
        # 平方损失
        left_loss = np.sum((left_y - left_pred) ** 2)
        right_loss = np.sum((right_y - right_pred) ** 2)
        total_loss = left_loss + right_loss
        
        return total_loss, left_pred, right_pred
    
    # 计算所有切分点的损失
    split_points = [1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5]
    
    print(f"{'切分点':<10} {'平方损失':<12} {'左侧预测':<10} {'右侧预测':<10}")
    print("-" * 45)
    
    for sp in split_points:
        loss, left_pred, right_pred = calculate_loss(X, y, sp)
        print(f"{sp:<10.1f} {loss:<12.4f} {left_pred:<10.4f} {right_pred:<10.4f}")
    
    # 3. 使用sklearn构建回归树
    print("\n=== 使用sklearn构建回归树 ===")
    reg = DecisionTreeRegressor(criterion='squared_error', max_depth=3, random_state=42)
    reg.fit(X, y)
    
    # 预测
    y_pred = reg.predict(X)
    print(f"预测值: {y_pred}")
    print(f"R²: {reg.score(X, y):.4f}")
    
    # 4. 可视化
    plt.figure(figsize=(12, 5))
    
    # 原始数据和预测
    plt.subplot(1, 2, 1)
    plt.scatter(X, y, color='blue', label='真实值')
    plt.scatter(X, y_pred, color='red', marker='^', label='预测值')
    X_test = np.linspace(1, 10, 100).reshape(-1, 1)
    y_test_pred = reg.predict(X_test)
    plt.plot(X_test, y_test_pred, color='green', label='回归树')
    plt.xlabel('X')
    plt.ylabel('y')
    plt.title('CART回归树')
    plt.legend()
    plt.grid(True)
    
    # 决策树结构
    plt.subplot(1, 2, 2)
    from sklearn.tree import plot_tree
    plot_tree(reg, feature_names=['X'], filled=True, rounded=True)
    plt.title('决策树结构')
    
    plt.tight_layout()
    plt.show()
    
    return reg

# 5. 对比不同深度
def compare_depths():
    """对比不同深度的回归树"""
    np.random.seed(42)
    X = np.sort(5 * np.random.rand(80, 1), axis=0)
    y = np.sin(X).ravel() + np.random.normal(0, 0.1, X.shape[0])
    
    X_test = np.linspace(0, 5, 200).reshape(-1, 1)
    
    depths = [1, 2, 3, 10]
    plt.figure(figsize=(15, 10))
    
    for i, depth in enumerate(depths, 1):
        reg = DecisionTreeRegressor(max_depth=depth, random_state=42)
        reg.fit(X, y)
        y_pred = reg.predict(X_test)
        
        plt.subplot(2, 2, i)
        plt.scatter(X, y, color='blue', s=20, label='训练数据')
        plt.plot(X_test, y_pred, color='red', label=f'深度={depth}')
        plt.xlabel('X')
        plt.ylabel('y')
        plt.title(f'决策树深度: {depth}')
        plt.legend()
        plt.grid(True)
    
    plt.tight_layout()
    plt.show()

# 运行示例
if __name__ == '__main__':
    print("=" * 50)
    print("CART回归树示例")
    print("=" * 50)
    cart_regression_demo()
    
    print("\n" + "=" * 50)
    print("不同深度对比")
    print("=" * 50)
    compare_depths()