梯度下降

-- codeing = utf-8 --

@Time :2021/4/12 20:25

@Author:sueong

@File:03.py

@Software:PyCharm

import numpy as np import matplotlib.pyplot as pltx_data=[1.0,2.0,3.0] y_data=[2.0,4.0,6.0] w=1.0#初始值假設為1.0 w=w-a*cost對w的偏導cost_list=[] epoch_list=[] def forword(x):return x*wdef cost(xs,ys):l_sum = 1for x,y in zip(x_data,y_data):y_pre = forword(x)l_sum+=(y_pre-y)**2return l_sum/len(xs)def gradient(xs,ys):grad=0for x, y in zip(x_data, y_data):y_pre = forword(x)grad+=2*x*(y_pre-y)return grad/len(xs)print('predict before traing',4,forword(4)) for epoch in range(100):epoch_list.append(epoch)cost_val=cost(x_data,y_data)cost_list.append(cost_val)grad_val=gradient(x_data,y_data)w-=0.01*grad_valprint('Epoch=',epoch,'w=',w,'loss',cost_val) print('predict(after training)',4,forword(4))plt.plot(epoch_list,cost_list) plt.ylabel('epoch') plt.xlabel('cost') plt.show()

隨機梯度下降

從左邊變成右邊這樣

# -*- codeing = utf-8 -*- # @Time :2021/4/12 20:58 # @Author:sueong # @File:Stochastic Gradient Descent.py # @Software:PyCharm # -*- codeing = utf-8 -*- # @Time :2021/4/12 20:25 # @Author:sueong # @File:03.py # @Software:PyCharm import numpy as np import matplotlib.pyplot as pltx_data=[1.0,2.0,3.0] y_data=[2.0,4.0,6.0] w=1.0#初始值假設為1.0 w=w-a*cost對w的偏導cost_list=[] epoch_list=[] def forword(x):return x*wdef loss(x,y):y_pre = forword(x)return (y_pre-y)**2def gradient(x,y):return 2*x*(x*w-y)print('predict before traing',4,forword(4)) for epoch in range(100):epoch_list.append(epoch)for x,y in zip(x_data,y_data):grad=gradient(x,y)#對每個樣本grad就更新ww=w-0.01*gradprint('\tgrad：',x,y,grad)l=loss(x,y)print('Epoch=',epoch,'w=',w,'loss',l)cost_list.append(l)print('predict(after training)',4,forword(4))plt.plot(epoch_list,cost_list) plt.ylabel('epoch') plt.xlabel('cost') plt.show()

總結

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