小试梯度下降算法

参考资料：

随机梯度下降法_通俗易懂讲解梯度下降法_weixin_39653442的博客-CSDN博客

梯度下降(Gradient Descent)_AI耽误的大厨的博客-CSDN博客

梯度下降法_踢开新世界的大门的博客-CSDN博客

仅做学习笔记

#给定样本求最佳 w 与 b
import matplotlib.pyplot as plot
import numpy as np#预测目标变量y的函数
def fun(w,b,x):f = w*x+breturn f#损失函数: J = 1/m*∑(f(x)-y)^2 其中f(x)=
#求导推理得
# w = w-alpha*1/m*∑[(f(x)-y)*x] 其中(f(x)-y)*x 为J对w的偏导
# b = b-alpha*1/m*∑[(f(x)-y)] 其中(f(x)-y) 为J对b的偏导#遍历整个样本数据，计算偏差，使用批量梯度下降法
def loopsum(w,b,x,y):m = len(x)w_sum = 0b_sum = 0loss_sum = 0for i in range(m):w_ = (fun(w,b,x[i])-y[i])*x[i]b_ = fun(w,b,x[i])-y[i]loss = b_*b_w_sum += w_b_sum += b_loss_sum += lossreturn (w_sum,b_sum,loss_sum)#批量梯度下降法更新w与b
def bacth_update_gradient(w,b,x,y,alpha):m = len(x)loss = 0w_tmp = (loopsum(w,b,x,y)[0]/m) while abs(w_tmp)>1e-5: #梯度近似于0，则不再更新w与b的值result = loopsum(w,b,x,y)w_tmp = (result[0]/m)b_tmp = (result[1]/m)loss  = (result[2]/m)w = w-alpha*w_tmpb = b-alpha*b_tmpreturn (w,b,loss)def main():#样本数据x = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]y = [1,4,7,4,1,6,7,3,9,6,11,10,13,14,11,16,19,18,19,20]alpha = 0.01 #学习率--步长w = 1 #初始化w值为1b = 1 #计算result = bacth_update_gradient(w,b,x,y,alpha)print(" w=%f\n b=%f\n loss=%f" %(result[0],result[1],result[2]))plot.figure(figsize=(6,4)) #新建6*4画布plot.scatter(x,y,label='y') #绘制散点图#plot.xlim(0,21)#plot.ylim(0,21)plot.xlabel('x',fontsize=20)plot.ylabel('y',fontsize=20)x=np.array(x)f=np.array(w*x+b)plot.plot(x,f,color ='red')#绘制拟合曲线plot.show()if __name__=="__main__":main()