非线性回归

import numpy as np
import random

'''''
梯度下降算法
参数说明：X，Y
theta:一组向量和x相乘的一组值
alpha:梯度下降时的参数，即每一步下降多少
m:实例的个数
numIteration：迭代计算的次数，可以理解为梯度下降多少步
'''
def gradientDescent(X,Y,theta,alpha,m,numIteration):
x_trains = X.transpose() #X的转置矩阵
for i in range(0,numIteration):
hypothesis = np.dot(X,theta) #内积形式，X与theta的乘积 ，求出y的估计值
loss = hypothesis - Y #估计值与真实值之间的差

    #通用的梯度下降算法，和logistic Regession中所描述的cost函数不一致  
    cos = np.sum(loss**2)/(2*m)  
    print "Iteration %d | Cost:%f" % (i,cos)  
      
    gradient = np.dot(x_trains,loss)/m  
    theta = theta - alpha*gradient  
      
return theta  

'''''
numPoints : 点的个数
bias :偏好ֵ
variance : 统计学概念， 偏差和
产生样本点和对应的标签
'''
def genData(numPoints,bias,variance):
X = np.zeros(shape=(numPoints,2)) #归类的数据
Y = np.zeros(shape=numPoints) #归类的标签

for i in range(0,numPoints):   #从0~len(numPoints)-1执行如下  
    X[i][0] = 1  
    X[i][1] = i  
    #制造target数据  
    Y[i] = (i+bias) + random.uniform(0,1)*variance  
      
return X,Y  

X,Y = genData(100, 25, 10)

print "X:",X

print "Y:",Y

m, n = np.shape(X)
n_y = np.shape(Y)

print "x shape :", m, " ", n

print "y length :",n_y

numIterations =100000
alpha = 0.0005
theta = np.ones(n)
theta = gradientDescent(X, Y, theta, alpha, m, numIterations)

print "theta: " ,theta