python
复制代码
import numpy as np
from matplotlib.font_manager import FontProperties
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt
class Lasso():
def __init__(self):
pass
# 数据准备
def prepare_data(self):
# 生成样本数据
X, y = make_regression(n_samples=40, n_features=80, random_state=0, noise=0.5)
# 划分数据集
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
return X_train, X_test, y_train.reshape(-1,1), y_test.reshape(-1,1)
# 参数初始化
def initialize_params(self, dims):
w = np.zeros((dims, 1))
b = 0
return w, b
# 定义L1损失函数
def l1_loss(self, X, y, w, b, alpha):
num_train = X.shape[0] # 样本数
num_feature = X.shape[1] # 特征数
y_hat = np.dot(X, w) + b # 回归预测数据
# 计算损失
loss = np.sum((y_hat - y) ** 2) / num_train + alpha * np.sum(np.abs(w)) # 修改此处
# 计算梯度,即参数的变化
dw = np.dot(X.T, (y_hat - y)) / num_train + alpha * np.sign(w) # 修改此处
db = np.sum((y_hat - y)) / num_train
return y_hat, loss, dw, db
def lasso_train(self, X, y, learning_rate, epochs, alpha):
loss_list = []
w, b = self.initialize_params(X.shape[1])
# 归一化特征
X = (X - np.mean(X, axis=0)) / np.std(X, axis=0)
for i in range(1, epochs):
y_hat, loss, dw, db = self.l1_loss(X, y, w, b, alpha)
# 更新参数
w += -learning_rate * dw
b += -learning_rate * db
loss_list.append(loss)
# if i % 300 == 0:
# print('epoch %d loss %f' % (i, loss))
params = {
'w': w,
'b': b
}
grads = {
'dw': dw,
'db': db
}
return loss, loss_list, params, grads
# 根据计算的得到的参数进行预测
def predict(self, X, params):
w = params['w']
b = params['b']
y_pred = np.dot(X, w) + b
return y_pred
if __name__ == '__main__':
lasso = Lasso()
X_train, X_test, y_train, y_test = lasso.prepare_data()
alphas=np.arange(0.01,0.11,0.01)
wc=[]#统计参数w中绝对值小于0.1的个数,模拟稀疏度
for alpha in alphas:
# 参数:训练集x,训练集y,学习率,迭代次数,正则化系数
loss, loss_list, params, grads = lasso.lasso_train(X_train, y_train, 0.02, 3000,alpha)
w=np.squeeze(params['w'])
count=np.sum(np.abs(w)<1e-1)
wc.append(count)
# 设置中文字体
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
plt.figure(figsize=(10, 8))
plt.plot(alphas, wc, 'o-')
plt.xlabel('正则项系数',fontsize=15)
plt.ylabel('参数w矩阵的稀疏度',fontsize=15)
plt.show()