Lasso和Elastic Net(弹性网络)在稀疏信号上的表现

翻译者:@Loopy
校验者:@barrycg

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。

  1. import numpy as np
  2. import matplotlib.pyplot as plt
  4. from sklearn.metrics import r2_score
  6. # 产生一些稀疏值
  7. np.random.seed(42)
  9. n_samples, n_features = 50, 100
  10. X = np.random.randn(n_samples, n_features)
  1. # 减少交替出现的符号以使其便于可视化
  2. idx = np.arange(n_features)
  3. coef = (-1) ** idx * np.exp(-idx / 10)
  4. coef[10:] = 0  # sparsify coef
  5. y = np.dot(X, coef)
  1. # 添加噪音
  2. y += 0.01 * np.random.normal(size=n_samples)
  1. # 划分测试,训练集
  2. n_samples = X.shape[0]
  3. X_train, y_train = X[:n_samples // 2], y[:n_samples // 2]
  4. X_test, y_test = X[n_samples // 2:], y[n_samples // 2:]
  1. # Lasso
  2. from sklearn.linear_model import Lasso
  4. alpha = 0.1
  5. lasso = Lasso(alpha=alpha)
  7. y_pred_lasso = lasso.fit(X_train, y_train).predict(X_test)
  8. r2_score_lasso = r2_score(y_test, y_pred_lasso)
  9. print(lasso)
  10. print("r^2 on test data : %f" % r2_score_lasso)
  1. Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,
  2.       normalize=False, positive=False, precompute=False, random_state=None,
  3.       selection='cyclic', tol=0.0001, warm_start=False)
  4. r^2 on test data : 0.658064
  1. # 弹性网络(ElasticNet)
  2. from sklearn.linear_model import ElasticNet
  4. enet = ElasticNet(alpha=alpha, l1_ratio=0.7)
  6. y_pred_enet = enet.fit(X_train, y_train).predict(X_test)
  7. r2_score_enet = r2_score(y_test, y_pred_enet)
  8. print(enet)
  9. print("r^2 on test data : %f" % r2_score_enet)
  1. ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.7,
  2.            max_iter=1000, normalize=False, positive=False, precompute=False,
  3.            random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
  4. r^2 on test data : 0.642515
  1. m, s, _ = plt.stem(np.where(enet.coef_)[0], enet.coef_[enet.coef_ != 0],
  2.                    markerfmt='x', label='Elastic net系数')
  3. plt.setp([m, s], color="#2ca02c")
  4. m, s, _ = plt.stem(np.where(lasso.coef_)[0], lasso.coef_[lasso.coef_ != 0],
  5.                    markerfmt='x', label='Lasso系数')
  6. plt.setp([m, s], color='#ff7f0e')
  7. plt.stem(np.where(coef)[0], coef[coef != 0], label='真实系数',
  8.          markerfmt='bx')
  10. plt.legend(loc='best')
  11. plt.title("Lasso $R^2$: %.3f, Elastic Net $R^2$: %.3f"
  12.           % (r2_score_lasso, r2_score_enet))
  13. plt.show()

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