Lasso 和 Elastic Net (弹性网络) 在稀疏信号上的表现

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2023-12-01

评估了 Lasso 回归模型和弹性网络回归模型在手动生成的，并附加噪声的稀疏信号上的表现，并将回归系数与真实值进行了比较。

import numpy as np
import matplotlib.pyplot as plt

from sklearn.metrics import r2_score

# 产生一些稀疏值
np.random.seed(42)

n_samples, n_features = 50, 100
X = np.random.randn(n_samples, n_features)

# 减少交替出现的符号以使其便于可视化
idx = np.arange(n_features)
coef = (-1) ** idx * np.exp(-idx / 10)
coef[10:] = 0  # sparsify coef
y = np.dot(X, coef)

# 添加噪音
y += 0.01 * np.random.normal(size=n_samples)

# 划分测试,训练集
n_samples = X.shape[0]
X_train, y_train = X[:n_samples // 2], y[:n_samples // 2]
X_test, y_test = X[n_samples // 2:], y[n_samples // 2:]

# Lasso
from sklearn.linear_model import Lasso

alpha = 0.1
lasso = Lasso(alpha=alpha)

y_pred_lasso = lasso.fit(X_train, y_train).predict(X_test)
r2_score_lasso = r2_score(y_test, y_pred_lasso)
print(lasso)
print("r^2 on test data : %f" % r2_score_lasso)

Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,
      normalize=False, positive=False, precompute=False, random_state=None,
      selection='cyclic', tol=0.0001, warm_start=False)
r^2 on test data : 0.658064

# 弹性网络(ElasticNet)
from sklearn.linear_model import ElasticNet

enet = ElasticNet(alpha=alpha, l1_ratio=0.7)

y_pred_enet = enet.fit(X_train, y_train).predict(X_test)
r2_score_enet = r2_score(y_test, y_pred_enet)
print(enet)
print("r^2 on test data : %f" % r2_score_enet)

ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.7,
           max_iter=1000, normalize=False, positive=False, precompute=False,
           random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
r^2 on test data : 0.642515

m, s, _ = plt.stem(np.where(enet.coef_)[0], enet.coef_[enet.coef_ != 0],
                   markerfmt='x', label='Elastic net系数')
plt.setp([m, s], color="#2ca02c")
m, s, _ = plt.stem(np.where(lasso.coef_)[0], lasso.coef_[lasso.coef_ != 0],
                   markerfmt='x', label='Lasso系数')
plt.setp([m, s], color='#ff7f0e')
plt.stem(np.where(coef)[0], coef[coef != 0], label='真实系数',
         markerfmt='bx')

plt.legend(loc='best')
plt.title("Lasso $R^2$: %.3f, Elastic Net $R^2$: %.3f"
          % (r2_score_lasso, r2_score_enet))
plt.show()