代码演示之正好拟合

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
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. 欠拟合（一次线性回归）
lr_under = LinearRegression()
lr_under.fit(X, Y)
y_pred_under = lr_under.predict(X)

# 3. 正好拟合（使用PolynomialFeatures增加复杂度）
# 3.1 创建多项式特征对象
poly = PolynomialFeatures(degree=3)
X_poly = poly.fit_transform(X)

# 3.2 训练模型
lr_good = LinearRegression()
lr_good.fit(X_poly, Y)

# 3.3 预测
y_pred_good = lr_good.predict(X_poly)

# 4. 绘图对比
plt.figure(figsize=(12, 5))

plt.subplot(1, 2, 1)
plt.scatter(X, Y, color='blue', label='数据点')
plt.plot(X, y_pred_under, color='red', label='欠拟合')
plt.title('欠拟合（一次）')
plt.legend()

plt.subplot(1, 2, 2)
plt.scatter(X, Y, color='blue', label='数据点')
plt.plot(X, y_pred_good, color='green', label='正好拟合')
plt.title('正好拟合（三次多项式）')
plt.legend()

plt.tight_layout()
plt.show()

# 5. 误差对比
print("欠拟合 MSE:", mean_squared_error(Y, y_pred_under))
print("正好拟合 MSE:", mean_squared_error(Y, y_pred_good))

def demo_fitting():
    """演示正好拟合"""
    # 1. 准备数据
    X = np.random.rand(30, 1) * 10
    Y = np.sin(X).ravel() + np.random.randn(30) * 0.1
    
    # 2. 数据预处理
    X = X.reshape(-1, 1)  # 转为列向量
    
    # 3. 生成多项式特征
    poly = PolynomialFeatures(degree=3)
    X_poly = poly.fit_transform(X)
    
    # 4. 模型训练
    model = LinearRegression()
    model.fit(X_poly, Y)
    
    # 5. 预测和评估
    y_pred = model.predict(X_poly)
    mse = mean_squared_error(Y, y_pred)
    
    print(f"权重W: {model.coef_}")
    print(f"偏置B: {model.intercept_}")
    print(f"MSE: {mse}")
    
    return model

# 运行
demo_fitting()