3、稀疏信号的LASSO与弹性网

import numpy as np

import matplotlib.pyplot as plt

from sklearn.metrics import r2_score

plt.rcParams['font.sans-serif'] = ['SimHei']

plt.rcParams['axes.unicode_minus'] = False

# 生成一些稀疏的数据

np.random.seed(42)

n_samples, n_features = 50, 100

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

# 降低coef w。可视化交替标志

idx = np.arange(n_features)

coef = (-1) ** idx * np.exp(-idx / 10)

coef[10:] = 0  # 稀疏 coef

y = np.dot(X, coef)

# 添加噪声

y += 0.01 * np.random.normal(size=n_samples)

# 拆分为训练/测试集

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)

# 弹性网

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)

m, s, _ = plt.stem(np.where(enet.coef_)[0], enet.coef_[enet.coef_ != 0],

                  markerfmt='x', label='Elastic net coefficients',

                  use_line_collection=True)

plt.setp([m, s], color="#2ca02c")

m, s, _ = plt.stem(np.where(lasso.coef_)[0], lasso.coef_[lasso.coef_ != 0],

                  markerfmt='x', label='Lasso coefficients',

                  use_line_collection=True)

plt.setp([m, s], color='#ff7f0e')

plt.stem(np.where(coef)[0], coef[coef != 0], label='true coefficients',

        markerfmt='bx', use_line_collection=True)

plt.legend(loc='best')

plt.title("Lasso $R^2$: %.3f, 弹性网 $R^2$: %.3f"

          % (r2_score_lasso, r2_score_enet))

plt.show()