优化分体为残差平方和最小，这是一个凸优化问题，使用cvxpy，过程过于简单。

    ##------数据生成部分----------##seed = 101X = np.random.uniform(low=1.0,high=10.0,size=300)y = X * 20 + 10 + np.random.normal(loc=0.0,scale=10.0,size=300)##--------凸优化部分-------------##w = cvx.Variable()b = cvx.Variable()objective = cvx.Minimize(cvx.sum_squares((w * X + b) - y))constrant = []prob = cvx.Problem(objective,[])prob.solve()##------结果可视化部分----------##print(w.value)print(b.value)show_data(X,y,w.value,b.value)plt.show()print("Loss=",np.mean(((w.value * X + b.value) - y)**2))

依赖cvxpy你就废了！你啥都学不到！

配上梯度下降方法计算出的对比。

'''
一元线性回归
代码可以正确运行，运行结果良好
'''
import numpy as np
import pandas as pd
import cvxpy as cvx
import matplotlib.pyplot as plt
import osclass LinearRegression(object):def __init__(self,learning_rate=0.01,max_iter=100,seed=101):self.w = np.random.randn(1)[0]self.b = np.random.randn(1)[0]self.lr = learning_rateself.max_iter = max_iterself.loss_arr = []def fit(self,X,y):self.X = Xself.y = yfor i in range(self.max_iter):self.Grandient_descent()self.loss_arr.append(self.loss())def model(self,X):return self.w * X + self.bdef loss(self,y_true=None,y_pred=None):if y_true is None or y_pred is None:y_true = self.yy_pred = self.model(self.X)return np.sum((y_true - y_pred) ** 2)def cal_gradient(self):d_w = np.sum(2 * (self.model(self.X) - self.y) * self.X)/len(self.X) #不理解为什么要取平均d_b = np.sum(2 * (self.model(self.X) - self.y))/len(self.X)   #不理解为什么要取平均return d_w, d_bdef Grandient_descent(self):d_w,d_b = self.cal_gradient()self.w -= self.lr * d_wself.b -= self.lr * d_bdef show_data(X,y,w=None,b=None):plt.scatter(X,y,marker='.')if w is not None and b is not None:plt.plot(X, X*w + b, c='r')if __name__ == '__main__':seed = 101X = np.random.uniform(low=1.0,high=10.0,size=300)y = X * 20 + 10 + np.random.normal(loc=0.0,scale=10.0,size=300)regr = LinearRegression(learning_rate=0.01, max_iter=100, seed=101)regr.fit(X,y)# plt.plot(np.arange(len(regr.loss_arr)),regr.loss_arr,marker='o',c='green')w = cvx.Variable()b = cvx.Variable()objective = cvx.Minimize(cvx.sum_squares((w * X + b) - y))constrant = []prob = cvx.Problem(objective, [])prob.solve()show_data(X, y, w.value, b.value)show_data(X, y, regr.w, regr.b)plt.show()print("Loss=", np.mean(((w.value * X + b.value) - y) ** 2))print(regr.loss_arr[-1]/len(X))

手动调整梯度下降迭代次数

max_iter=100

迭代次数越大，梯度下降的计算结果越贴近cvxpy的优化结果。