Lasso原理

Lasso与弹性拟合比较python实现

import numpy as npimport matplotlib.pyplot as pltfrom sklearn.metrics import r2_score#def main():# 产生一些稀疏数据np.random.seed(42)n_samples, n_features = 50, 200X = np.random.randn(n_samples, n_features) # randn(...)产生的是正态分布的数据coef = 3 * np.random.randn(n_features) # 每个特征对应一个系数inds = np.arange(n_features)np.random.shuffle(inds)coef[inds[10:]] = 0 # 稀疏化系数--随机的把系数向量1x200的其中10个值变为0y = np.dot(X, coef) # 线性运算 -- y = X.*w# 添加噪声：零均值，标准差为 0.01 的高斯噪声y += 0.01 * np.random.normal(size=n_samples)# 把数据划分成训练集和测试集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:]# 训练 Lasso 模型from sklearn.linear_model import Lassoalpha = 0.1lasso = 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)# 训练 ElasticNet 模型from sklearn.linear_model import ElasticNetenet = 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)plt.plot(enet.coef_, color='lightgreen', linewidth=2, label='Elastic net coefficients')plt.plot(lasso.coef_, color='gold', linewidth=2, label='Lasso coefficients')plt.plot(coef, '--', color='navy', label='original coefficients')plt.legend(loc='best')plt.title("Lasso R^2: %f, Elastic Net R^2: %f" % (r2_score_lasso, r2_score_enet))plt.show()

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总结

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