代码演示之欠拟合

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

# 生成数据
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

# 1. 欠拟合（一次线性回归）
lr_under = LinearRegression()
lr_under.fit(X, Y)
y_pred_under = lr_under.predict(X)

# 2. 正好拟合（三次多项式）
poly_features = PolynomialFeatures(degree=3)
X_poly = poly_features.fit_transform(X)
lr_good = LinearRegression()
lr_good.fit(X_poly, Y)
y_pred_good = lr_good.predict(X_poly)

# 3. 过拟合（20次多项式）
poly_over = PolynomialFeatures(degree=20)
X_poly_over = poly_over.fit_transform(X)
lr_over = LinearRegression()
lr_over.fit(X_poly_over, Y)
y_pred_over = lr_over.predict(X_poly_over)

# 绘图
plt.figure(figsize=(15, 5))

plt.subplot(1, 3, 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, 3, 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）')
plt.legend()

plt.subplot(1, 3, 3)
plt.scatter(X, Y, color='blue', label='数据点')
plt.plot(X, y_pred_over, color='purple', label='过拟合')
plt.title('过拟合（20次）')
plt.legend()

plt.tight_layout()
plt.show()

# 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))
print("过拟合 MSE:", mean_squared_error(Y, y_pred_over))