Python案例如何用Scikit-learn做弹性网络

wen python案例 2026-07-16 257

本文目录导读：

弹性网络简介
完整案例代码
关键参数说明
实际应用示例
注意事项

我来详细介绍如何使用Scikit-learn实现弹性网络（Elastic Net）回归，包括完整的案例代码。

弹性网络简介

弹性网络结合了L1（Lasso）和L2（Ridge）正则化，适用于特征数量多于样本数量或特征间存在相关性的情况。

完整案例代码

数据生成与模型训练

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, cross_val_score, GridSearchCV
from sklearn.linear_model import ElasticNet
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error
import warnings
warnings.filterwarnings('ignore')
# 设置中文显示
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
# 1. 生成示例数据
print("="*50)
print("1. 生成示例数据")
print("="*50)
# 生成具有噪声的回归数据
np.random.seed(42)
X, y, true_coef = make_regression(
    n_samples=200,  # 样本数量
    n_features=20,  # 特征数量
    n_informative=10,  # 有用的特征数量
    noise=20,  # 噪声水平
    coef=True,  # 返回真实系数
    random_state=42
)
print(f"数据形状: X: {X.shape}, y: {y.shape}")
print(f"真实系数非零个数: {np.sum(true_coef != 0)}")
print(f"前10个真实系数: {true_coef[:10]}")
# 2. 数据预处理
print("\n" + "="*50)
print("2. 数据预处理")
print("="*50)
# 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)
# 标准化特征
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)
print(f"训练集大小: {X_train.shape[0]} 样本")
print(f"测试集大小: {X_test.shape[0]} 样本")
# 3. 使用默认参数训练ElasticNet
print("\n" + "="*50)
print("3. 基础ElasticNet模型")
print("="*50)
# 创建弹性网络模型
# alpha: 正则化强度 (越大正则化越强)
# l1_ratio: L1正则化比例 (0=Ridge, 1=Lasso)
elastic_net = ElasticNet(
    alpha=1.0,
    l1_ratio=0.5,
    random_state=42,
    max_iter=10000
)
# 训练模型
elastic_net.fit(X_train_scaled, y_train)
# 预测
y_pred_train = elastic_net.predict(X_train_scaled)
y_pred_test = elastic_net.predict(X_test_scaled)
# 评估模型
print(f"训练集 R²: {r2_score(y_train, y_pred_train):.4f}")
print(f"测试集 R²: {r2_score(y_test, y_pred_test):.4f}")
print(f"测试集 MSE: {mean_squared_error(y_test, y_pred_test):.4f}")
print(f"测试集 MAE: {mean_absolute_error(y_test, y_pred_test):.4f}")
print(f"非零系数个数: {np.sum(elastic_net.coef_ != 0)}")
# 4. 超参数调优
print("\n" + "="*50)
print("4. 超参数调优 (GridSearchCV)")
print("="*50)
# 定义参数网格
param_grid = {
    'alpha': [0.001, 0.01, 0.1, 1.0, 10.0],
    'l1_ratio': [0.1, 0.3, 0.5, 0.7, 0.9, 1.0]
}
# 创建ElasticNet模型
elastic_net_base = ElasticNet(random_state=42, max_iter=10000)
# 网格搜索
grid_search = GridSearchCV(
    estimator=elastic_net_base,
    param_grid=param_grid,
    scoring='r2',
    cv=5,
    n_jobs=-1,
    verbose=1
)
# 执行网格搜索
grid_search.fit(X_train_scaled, y_train)
print(f"最佳参数: {grid_search.best_params_}")
print(f"最佳交叉验证得分: {grid_search.best_score_:.4f}")
# 5. 使用最佳参数训练模型
print("\n" + "="*50)
print("5. 优化后的模型")
print("="*50)
best_elastic = grid_search.best_estimator_
y_pred_best = best_elastic.predict(X_test_scaled)
print(f"优化后测试集 R²: {r2_score(y_test, y_pred_best):.4f}")
print(f"优化后测试集 MSE: {mean_squared_error(y_test, y_pred_best):.4f}")
print(f"非零系数个数: {np.sum(best_elastic.coef_ != 0)}")
# 6. 交叉验证
print("\n" + "="*50)
print("6. 交叉验证评估")
print("="*50)
cv_scores = cross_val_score(best_elastic, X_train_scaled, y_train, cv=5, scoring='r2')
print(f"交叉验证 R² 得分: {cv_scores}")
print(f"平均 R²: {cv_scores.mean():.4f} (+/- {cv_scores.std() * 2:.4f})")
# 7. 特征重要性分析
print("\n" + "="*50)
print("7. 特征重要性分析")
print("="*50)
# 获取特征系数
feature_importance = pd.DataFrame({
    'feature': [f'Feature_{i}' for i in range(X.shape[1])],
    'coefficient': best_elastic.coef_
})
feature_importance['abs_coefficient'] = np.abs(feature_importance['coefficient'])
feature_importance = feature_importance.sort_values('abs_coefficient', ascending=False)
print("重要特征 (Top 10):")
print(feature_importance.head(10))
print(f"\n零系数特征个数: {np.sum(best_elastic.coef_ == 0)}")
# 8. 可视化
print("\n" + "="*50)
print("8. 可视化分析")
print("="*50)
fig, axes = plt.subplots(2, 3, figsize=(15, 10))
# 8.1 真实值 vs 预测值
axes[0, 0].scatter(y_test, y_pred_best, alpha=0.6, edgecolors='k')
axes[0, 0].plot([y.min(), y.max()], [y.min(), y.max()], 'r--', lw=2)
axes[0, 0].set_xlabel('真实值')
axes[0, 0].set_ylabel('预测值')
axes[0, 0].set_title(f'真实值 vs 预测值 (R² = {r2_score(y_test, y_pred_best):.4f})')
axes[0, 0].grid(True, alpha=0.3)
# 8.2 残差图
residuals = y_test - y_pred_best
axes[0, 1].scatter(y_pred_best, residuals, alpha=0.6, edgecolors='k')
axes[0, 1].axhline(y=0, color='r', linestyle='--', lw=2)
axes[0, 1].set_xlabel('预测值')
axes[0, 1].set_ylabel('残差')
axes[0, 1].set_title('残差图')
axes[0, 1].grid(True, alpha=0.3)
# 8.3 系数比较
axes[0, 2].plot(true_coef, 'o-', label='真实系数', alpha=0.7)
axes[0, 2].plot(best_elastic.coef_, 's-', label='弹性网络系数', alpha=0.7)
axes[0, 2].set_xlabel('特征索引')
axes[0, 2].set_ylabel('系数值')
axes[0, 2].set_title('系数比较')
axes[0, 2].legend()
axes[0, 2].grid(True, alpha=0.3)
# 8.4 不同alpha值的表现
alphas = [0.001, 0.01, 0.1, 1.0, 10.0]
r2_scores_alpha = []
non_zero_coefs = []
for alpha in alphas:
    en = ElasticNet(alpha=alpha, l1_ratio=0.5, random_state=42, max_iter=10000)
    en.fit(X_train_scaled, y_train)
    y_pred = en.predict(X_test_scaled)
    r2_scores_alpha.append(r2_score(y_test, y_pred))
    non_zero_coefs.append(np.sum(en.coef_ != 0))
axes[1, 0].semilogx(alphas, r2_scores_alpha, 'o-', linewidth=2)
axes[1, 0].set_xlabel('Alpha (对数尺度)')
axes[1, 0].set_ylabel('R² 得分')
axes[1, 0].set_title('不同Alpha值的R²得分')
axes[1, 0].grid(True, alpha=0.3)
# 8.5 不同l1_ratio值的表现
l1_ratios = [0.1, 0.3, 0.5, 0.7, 0.9, 1.0]
r2_scores_l1 = []
non_zero_coefs_l1 = []
for l1_ratio in l1_ratios:
    en = ElasticNet(alpha=0.1, l1_ratio=l1_ratio, random_state=42, max_iter=10000)
    en.fit(X_train_scaled, y_train)
    y_pred = en.predict(X_test_scaled)
    r2_scores_l1.append(r2_score(y_test, y_pred))
    non_zero_coefs_l1.append(np.sum(en.coef_ != 0))
axes[1, 1].plot(l1_ratios, r2_scores_l1, 'o-', linewidth=2, label='R²得分')
axes[1, 1].plot(l1_ratios, non_zero_coefs_l1, 's-', linewidth=2, label='非零系数')
axes[1, 1].set_xlabel('L1 Ratio')
axes[1, 1].set_ylabel('数值')
axes[1, 1].set_title('不同L1 Ratio的表现')
axes[1, 1].legend()
axes[1, 1].grid(True, alpha=0.3)
# 8.6 特征重要性条形图
top_10_features = feature_importance.head(10)
axes[1, 2].barh(range(10), top_10_features['coefficient'].values, 
                color=['red' if x < 0 else 'blue' for x in top_10_features['coefficient']])
axes[1, 2].set_yticks(range(10))
axes[1, 2].set_yticklabels(top_10_features['feature'].values)
axes[1, 2].set_xlabel('系数值')
axes[1, 2].set_title('Top 10 特征重要性')
axes[1, 2].axvline(x=0, color='k', linestyle='-', linewidth=0.5)
axes[1, 2].grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
# 9. 模型比较
print("\n" + "="*50)
print("9. 模型比较 (默认vs优化)")
print("="*50)
models_comparison = pd.DataFrame({
    '模型': ['默认ElasticNet', '优化ElasticNet'],
    '训练集R²': [r2_score(y_train, y_pred_train), 
                 r2_score(y_train, best_elastic.predict(X_train_scaled))],
    '测试集R²': [r2_score(y_test, y_pred_test), r2_score(y_test, y_pred_best)],
    '非零系数': [np.sum(elastic_net.coef_ != 0), np.sum(best_elastic.coef_ != 0)]
})
print(models_comparison.to_string(index=False))

关键参数说明

主要参数

alpha: 正则化强度参数（λ），控制整体正则化程度
- alpha越大,正则化越强，模型越简单
- alpha越小,模型更复杂，容易过拟合
l1_ratio: L1正则化的比例（ρ）
- l1_ratio=0: 纯Ridge回归
- l1_ratio=1: 纯Lasso回归
- 0<l1_ratio<1: 弹性网络

参数选择建议

# 对于高维稀疏数据的参数选择
params_sparse = {
    'alpha': [0.001, 0.01, 0.1],  # 较小的alpha
    'l1_ratio': [0.7, 0.9, 1.0]   # 接近Lasso
}
# 对于数据相关性强的参数选择
params_correlated = {
    'alpha': [0.1, 1.0, 10.0],    # 较大的alpha
    'l1_ratio': [0.2, 0.4, 0.6]   # 平衡L1和L2
}

实际应用示例

使用真实数据集

from sklearn.datasets import load_diabetes
# 加载糖尿病数据集
diabetes = load_diabetes()
X, y = diabetes.data, diabetes.target
# 创建弹性网络模型
elastic = ElasticNet(alpha=0.1, l1_ratio=0.5)
# 训练和评估
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
elastic.fit(X_train, y_train)
print(f"测试集R²: {elastic.score(X_test, y_test):.4f}")