非線性回歸應(yīng)用（Logistic Regression Application）

import numpy as np import random# 一個(gè)函數(shù)為梯度下降的算法 def GradientDescent(x,y,theta,alpha,m,numInterations):# m denotes the number of examples here, not the number of features'''x:實(shí)例；y：分類標(biāo)簽theta：要學(xué)習(xí)的參數(shù)θalpha：learning ratem：更新法則公式中實(shí)例的個(gè)數(shù),對(duì)應(yīng)矩陣的維數(shù)[]numInterations：使用此方法循環(huán)訓(xùn)練更新的次數(shù)'''xTrans = x.transpose() #轉(zhuǎn)置x便于后面運(yùn)算for i in range(0,numInterations):hypothesis = np.dot(x,theta) #這里為什么要放在for循環(huán)里面，并不受循環(huán)影響？ #for循環(huán)次數(shù)即為更新次數(shù)loss = hypothesis - y #hypothesis其實(shí)就是y_hat,這里loss就等于y_hat減去y(實(shí)際)# avg cost per example (the 2 in 2*m doesn't really matter here.# But to be consistent with the gradient, I include itcost = np.sum(loss**2)/(2*m)#這里的cost函數(shù)與課文中提到的cost函數(shù)不一樣，這里使用了一個(gè)簡(jiǎn)單的cost便于計(jì)算'''cost：對(duì)精確度的衡量，每一次gradient都會(huì)減小'''print('Interation:%d|cost:%f'%(i,cost))# avg gradient per examplegradient = np.dot(xTrans,loss)/m #每一次的下降梯度值,除以m：取平均# updatatheta = theta-alpha*gradient #即更新法則的公式：θ=θ-α∑(h(x)-y)xreturn theta# 一個(gè)函數(shù)用來(lái)產(chǎn)生數(shù)據(jù)用來(lái)測(cè)試擬合 def genData(numPoints,bias,variance):'''numPoints:實(shí)例的行數(shù)（矩陣形式，每一行對(duì)應(yīng)一對(duì)實(shí)例）bias:生成y時(shí)產(chǎn)生一個(gè)偏差值variance:方差'''x = np.zeros(shape=(numPoints,2)) #numPoints行，2列的矩陣y = np.zeros(shape=(numPoints))#basically a staight linefor i in range(0,numPoints):# bias featurex[i][0] = 1x[i][1] = i# target variabley[i] = (i+bias)+random.uniform(0,1)*variance #random.uniform(0,1)同random.random()產(chǎn)生0~1隨機(jī)數(shù)return x,y# generate 100 columns with a bias of 25 and 10 variance as a bit of noise x,y = genData(100,25,10)#前面函數(shù)返回了兩個(gè)變量x，y此處可以任意取兩個(gè)變量按偏移量賦值給返回的x和y # print(x) # print(y) m,n = np.shape(x) #x的行數(shù)賦值給m，列數(shù)賦值為n a = np.shape(y) #y只有一列不會(huì)返回列的數(shù)值，會(huì)返回行的數(shù)值 # print(m,n) #(100行，2列) # print(a) #(100行，1列)numInterations = 100000 alpha = 0.0005 #取0~1，比較好的算法會(huì)設(shè)置開(kāi)始的alpha數(shù)值較大后期數(shù)值較小 theta = np.ones(n) # 初始化θ：[1. 1.] 為什么設(shè)置為1? theta = GradientDescent(x,y,theta,alpha,m,numInterations) print(theta) #約為[30 1]# 得出的theta就可以用于對(duì)新實(shí)例的計(jì)算和預(yù)測(cè) #回歸算法和神經(jīng)網(wǎng)絡(luò)中都會(huì)用到此梯度下降的方法

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