ML之UliR：利用非線性回歸，梯度下降法(疊代十萬次)求出學習參數θ，進而求得Cost函數最優值

輸出結果

更新……

代碼設計

import numpy as np  

import random      

def genData(numPoints,bias,variance):  

   x = np.zeros(shape=(numPoints,2))

   y = np.zeros(shape=(numPoints))  

   for i in range(0,numPoints):    

       x[i][0]=1                

       x[i][1]=i                  

       y[i]=(i+bias)+random.uniform(0,1)%variance

   return x,y

def gradientDescent(x,y,theta,alpha,m,numIterations):

   xTran = np.transpose(x)        

   for i in range(numIterations):

       hypothesis = np.dot(x,theta)

       loss = hypothesis-y      

       cost = np.sum(loss**2)/(2*m)

       gradient=np.dot(xTran,loss)/m

       theta = theta-alpha*gradient

       print ("Iteration %d | cost :%f" %(i,cost))

   return theta

x,y = genData(100, 25, 10)  #100行，

print ("x:")

print (x)

print ("y:")

print (y)

m,n = np.shape(x)

n_y = np.shape(y)  

print("m:"+str(m)+" n:"+str(n)+" n_y:"+str(n_y))

numIterations = 100000    

alpha = 0.0005          

theta = np.ones(n)    

theta= gradientDescent(x, y, theta, alpha, m, numIterations)

print(theta)