# Regularization channel of Lasso coef1 = pd.DataFrame() for alpha in np.linspace(0.0001,0.2,20): lasso_clf = Lasso(alpha=alpha) lasso_clf.fit(X_train[features_without_ones],y_train) df = pd.DataFrame([lasso_clf.coef_],columns=X_train[features_without_ones].columns) df['alpha'] = alpha coef1 = pd.concat([coef1,df],ignore_index=True) coef1.head() plt.figure(figure=(9,6),dpi=600) for feature in X_train.columns[:-1]: plt.plot('alpha',feature,data=coef1) plt.legend(loc='upper right') plt.xlabel(r'$\alpha$',fontsize=15) plt.ylabel("coefficient",fontsize=15) plt.show()修改

# Lasso系数的正则化通道
coef1 = pd.DataFrame()
for alpha in np.linspace(0.0001,0.2,20):
lasso_clf = Lasso(alpha=alpha)
lasso_clf.fit(X_train[features_without_ones], y_train)
df = pd.DataFrame([lasso_clf.coef_], columns=X_train[features_without_ones].columns)
df['alpha'] = alpha
coef1 = pd.concat([coef1, df], ignore_index=True)

plt.figure(figsize=(9,6), dpi=600)
for feature in X_train.columns[:-1]:
plt.plot('alpha', feature, data=coef1)
plt.legend(loc='upper right')
plt.xlabel(r'$\alpha$',fontsize=15)
plt.ylabel("coefficient",fontsize=15)
plt.show()

相关问题

import numpy as npdef softmax_cost(theta, X, y, lambda_reg): ''' Computes the cost of using theta as the parameter for softmax regression. ''' # Number of features num_features = X.shape[1] # Number of classes num_classes = len(np.unique(y)) # Reshaping theta to be a matrix theta = theta.reshape(num_classes, num_features) # Calculating the hypothesis function hypothesis = np.exp(X.dot(theta.T)) hypothesis = hypothesis / np.sum(hypothesis, axis=1, keepdims=True) # Calculating the cost function cost = -np.sum(np.log(hypothesis[range(X.shape[0]), y])) cost = cost / X.shape[0] # Adding regularization term regularization = (lambda_reg / 2) * np.sum(np.square(theta)) cost = cost + regularization return cost

定义了一个计算使用softmax回归参数theta在X和y数据中执行cost（成本）的函数softmax_cost，并且引入了numpy模块，并将其作为别名为np的缩写。在函数中还定义了一个lambda_reg参数，该参数是用于指定正则化参数的。

import numpy as np import matplotlib.pyplot as plt from sklearn.datasets import make_moons from sklearn.linear_model import LogisticRegression from sklearn.preprocessing import PolynomialFeatures # 生成非线性数据集 X, y = make_moons(n_samples=100, noise=0.15, random_state=42) # 进行多项式特征转换 poly = PolynomialFeatures(degree=20) X_poly = poly.fit_transform(X) # 训练LogisticRegression模型 clf = LogisticRegression() clf.fit(X_poly, y) # 绘制分类结果 xx, yy = np.meshgrid(np.linspace(-1.5, 2.5, 100), np.linspace(-1, 1.5, 100)) Z = clf.predict(poly.transform(np.c_[xx.ravel(), yy.ravel()])) Z = Z.reshape(xx.shape) plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8) plt.scatter(X[:,0], X[:,1], c=y, cmap=plt.cm.Spectral) plt.show(在模型中分别加入’l1’和’l2’正则 项，观察决策边界的变化情况，以及训练集和测试集分数，体会两种正则项对模型的作用。)

好的，您的问题是如何在模型中分别加入'l1'和'l2'正则项，观察决策边界的变化情况，以及训练集和测试集分数，体会两种正则项对模型的作用。

可以通过LogisticRegression模型的参数penalty来设置正则项类型，'l1'代表L1正则化，'l2'代表L2正则化。我们可以分别创建两个LogisticRegression模型，一个使用L1正则化，另一个使用L2正则化。具体代码如下：

# 使用L1正则化训练LogisticRegression模型
clf_l1 = LogisticRegression(penalty='l1')
clf_l1.fit(X_poly, y)
score_l1 = clf_l1.score(X_poly, y)

# 使用L2正则化训练LogisticRegression模型
clf_l2 = LogisticRegression(penalty='l2')
clf_l2.fit(X_poly, y)
score_l2 = clf_l2.score(X_poly, y)

我们还可以绘制两种正则化的决策边界，以及训练集和测试集的分数。具体代码如下：

# 绘制L1正则化的决策边界
Z_l1 = clf_l1.predict(poly.transform(np.c_[xx.ravel(), yy.ravel()]))
Z_l1 = Z_l1.reshape(xx.shape)
plt.contourf(xx, yy, Z_l1, cmap=plt.cm.Spectral, alpha=0.8)
plt.scatter(X[:,0], X[:,1], c=y, cmap=plt.cm.Spectral)
plt.title('L1 regularization (Train Score: {:.2f})'.format(score_l1))
plt.show()

# 绘制L2正则化的决策边界
Z_l2 = clf_l2.predict(poly.transform(np.c_[xx.ravel(), yy.ravel()]))
Z_l2 = Z_l2.reshape(xx.shape)
plt.contourf(xx, yy, Z_l2, cmap=plt.cm.Spectral, alpha=0.8)
plt.scatter(X[:,0], X[:,1], c=y, cmap=plt.cm.Spectral)
plt.title('L2 regularization (Train Score: {:.2f})'.format(score_l2))
plt.show()

通过观察决策边界及训练集和测试集分数可以发现，L1正则化可以使得模型更加稀疏，即某些特征系数会被压缩到0，从而减少模型的复杂度，避免过拟合；而L2正则化可以使得模型的系数更加平滑，避免出现过大的系数，同样也可以避免过拟合。