代码演示之过拟合

X = np.array([1, 2, 3])
X2 = X ** 2  # [1, 4, 9]
X3 = X ** 3  # [1, 8, 27]

# 水平拼接
X_combined = np.hstack([X, X2, X3])

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

# 1. 准备数据
np.random.seed(42)
X = np.sort(np.random.rand(30, 1) * 10, axis=0)
Y = np.sin(X).ravel() + np.random.randn(30) * 0.1

# 2. 模拟过拟合（新增9列特征）
def demo_overfitting():
    """演示过拟合"""
    # 原始特征
    X_base = X.ravel()
    
    # 新增特征列 X²~X⁹
    features = [X_base]
    for i in range(2, 10):
        features.append(X_base ** i)
    
    # 水平拼接
    X_over = np.vstack(features).T  # 30行9列
    
    print(f"处理后的特征形状: {X_over.shape}")
    print(f"特征数: {X_over.shape[1]}")
    
    # 训练模型
    model = LinearRegression()
    model.fit(X_over, Y)
    
    # 预测
    y_pred = model.predict(X_over)
    
    # 评估
    mse = mean_squared_error(Y, y_pred)
    print(f"过拟合 MSE: {mse}")
    
    return X_over, y_pred

# 运行
X_over, y_pred_over = demo_overfitting()

# 3. 三种拟合对比绘图
plt.figure(figsize=(15, 5))

# 欠拟合
plt.subplot(1, 3, 1)
lr1 = LinearRegression()
lr1.fit(X, Y)
plt.scatter(X, Y, color='blue', s=10)
plt.plot(X, lr1.predict(X), color='red')
plt.title('欠拟合（1次）')

# 正好拟合
plt.subplot(1, 3, 2)
from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=3)
X_poly = poly.fit_transform(X)
lr2 = LinearRegression()
lr2.fit(X_poly, Y)
plt.scatter(X, Y, color='blue', s=10)
plt.plot(X, lr2.predict(X_poly), color='green')
plt.title('正好拟合（3次）')

# 过拟合
plt.subplot(1, 3, 3)
plt.scatter(X, Y, color='blue', s=10)
plt.plot(X, y_pred_over, color='purple')
plt.title('过拟合（9次）')

plt.tight_layout()
plt.show()