解析python实现Lasso回归
Lasso原理
Lasso与弹性拟合比较python实现
import numpy as np import matplotlib.pyplot as plt from sklearn.metrics import r2_score #def main(): # 产生一些稀疏数据 np.random.seed(42) n_samples, n_features = 50, 200 X = 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0 y = 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 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) # 训练 ElasticNet 模型 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) 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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