1. 基本模型

测试数据为X（x0，x1，x2···xn）

要学习的参数为： Θ（θ0，θ1，θ2，···θn）

2. Cost函数

线性回归:

非线性回归 Logistic regression:

目标：找到合适的 θ0，θ1使上式最小

3.解法：梯度下降（gradient decent)

更新法则：

学习率：
同时对所有的θ进行更新，重复更新直到收敛

4.代码

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)
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)

            【注】：本文为麦子学院机器学习课程的学习笔记