1. 基本模型
測試數(shù)據(jù)為X（x0何恶，x1寄啼，x2···xn）
要學(xué)習(xí)的參數(shù)為： Θ（θ0恩够，θ1背率，θ2话瞧，···θn）
2. Cost函數(shù)
線性回歸:
非線性回歸 Logistic regression:
目標(biāo)：找到合適的 θ0，θ1使上式最小
3.解法：梯度下降（gradient decent)
更新法則：
學(xué)習(xí)率：
同時(shí)對(duì)所有的θ進(jìn)行更新寝姿，重復(fù)更新直到收斂
4.代碼
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】：本文為麥子學(xué)院機(jī)器學(xué)習(xí)課程的學(xué)習(xí)筆記
