R码在增广后向消去变量选择中的应用

import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from statsmodels.stats.outliers_influence import variance_inflation_factor

# 示例数据
data = pd.DataFrame({
    'x1': np.random.rand(100),
    'x2': np.random.rand(100),
    'x3': np.random.rand(100),
    'y': 2 * data['x1'] + 3 * data['x2'] + np.random.randn(100)
})

# 划分训练集和测试集
X = data[['x1', 'x2', 'x3']]
y = data['y']
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# 初始模型
model = LinearRegression()
model.fit(X_train, y_train)
r2_initial = model.score(X_test, y_test)

# 增广后向消去变量选择
variables = X.columns.tolist()
while len(variables) > 1:
    r2_values = []
    for var in variables:
        X_temp = X_train.drop(columns=[var])
        model.fit(X_temp, y_train)
        r2_values.append((var, model.score(X_test.drop(columns=[var]), y_test)))
    var_to_remove, _ = min(r2_values, key=lambda x: x[1])
    variables.remove(var_to_remove)

# 最终模型
final_model = LinearRegression()
final_model.fit(X_train[variables], y_train)
r2_final = final_model.score(X_test[variables], y_test)

print(f"Initial R^2: {r2_initial}")
print(f"Final R^2: {r2_final}")
print(f"Selected Variables: {variables}")