前一篇已經總結了梯度下降法，今天嘗試將代碼用Python實現，之所以選擇Python是因爲用python寫的代碼可以短一些=。=
如果哪裏不對了，希望可以幫我糾正~~
首先是批量隨機梯度法，適用於訓練樣本數目不是特別多的情況，而且可以用於樣本特徵數目n更多的情況：
# -*- coding: cp936 -*-
#Training data set
#-----by plz
import numpy as np
def linear_regression(data_x,data_y,m,n,alpha):
ones=np.ones(m)
data_x=np.column_stack((data_x,ones))
theta_guess=np.ones(n+1) #有n個特徵，theta就是n+1維
x_trans=data_x.transpose() #data_x的轉置矩陣
theta_last=np.zeros(n+1)
theta_loss=theta_guess-theta_last
theta_losssq=np.sum(theta_loss**2)
while(np.sum((theta_guess-theta_last)**2)>0.0000000001):
print "np.sum((theta_guess-theta_last)**2) is:" , np.sum((theta_guess-theta_last)**2)
theta_last=theta_guess
hypothesis=np.dot(data_x,theta_guess)
loss=hypothesis-data_y
cost = np.sum(loss ** 2)
print "cost is" , cost
gradient=np.dot(x_trans,loss)
theta_guess=theta_guess-alpha*gradient
return theta_guess
data_x=np.array([(0,1),(1,2),(2,3)])
data_y=np.array([4.9,7.8,11.3])
m=data_x.shape[0] #訓練樣本數
n=data_x.shape[1] #樣本特徵數
alpha=0.001
theta=linear_regression(data_x,data_y,m,n,alpha)
print theta其次是隨機梯度下降法，適用於樣本數目成千上萬的情況，相比批量梯度下降法，隨機梯度下降法只能在最優值附近徘徊，並不能收斂到最優，不過由於它的速度比較快，效果也還不錯~
#------by plz
import numpy as np
def linear_regression(data_x,data_y,m,n,alpha):
theta=np.ones(n+1)
for j in range(1,m):
hypothesis=np.dot(data_x[j],theta)
loss=hypothesis-data_y[j]
gradient=np.dot(loss,data_x[j])
theta=theta-alpha*gradient
return theta
#這裏只是用11個樣本的數據集舉個例子,實際上需要大量樣本
data_x=np.array([0,1,2,3,4,5,6,7,8,9,10])
data_y=np.array([95.3,97.2,60.1,49.34,37.4,51.05,25.5,5.25,0.63,-9.4,-4.38])
m=11
n=1
theta=linear_regression(data_x,data_y,m,n,0.001)
print theta哪裏不對了一定要提出來~一起進步~
