原文地址：http://www.jianshu.com/p/311141f2047d

问题描述

程序实现

13-15

# coding: utf-8

import numpy as np

import numpy.random as random

import matplotlib.pyplot as plt

def sign(x):

    if(x>=0):

        return 1

    else:

        return -1

def gen_data():

    x1=random.uniform(-1,1,1000)

    x2=random.uniform(-1,1,1000)

    id_array=random.permutation([i for i in range(1000)])

    dataY=np.zeros((1000,1))

    for i in range(1000):

        if(i<1000*0.1):

            i = id_array[i]

            dataY[i][0]=-sign(x1[i]**2+x2[i]**2-0.6)

        else:

            i = id_array[i]

            dataY[i][0]=sign(x1[i]**2+x2[i]**2-0.6)

    dataX=np.concatenate((np.ones((1000,1)),np.array(x1).reshape((1000,1)),np.array(x2).reshape((1000,1))),axis=1)

    return dataX,dataY

def w_lin(dataX,dataY):

    dataX_T=np.transpose(dataX)

    tmp=np.dot(np.linalg.inv(np.dot(dataX_T,dataX)),dataX_T)

    return np.dot(tmp,dataY)

def pred(dataX,wLIN):

    pred=np.dot(dataX,wLIN)

    num_data=dataX.shape[0]

    for i in range(num_data):

        pred[i][0]=sign(pred[i][0])

    return pred

def zero_one_cost(pred,dataY):

    return np.sum(pred!=dataY)/dataY.shape[0]

def feat_transform(dataX):

    num_data=dataX.shape[0]

    tmp1=dataX[:,1]*dataX[:,2]

    tmp2=dataX[:,1]**2

    tmp3=dataX[:,2]**2

    new_dataX=np.concatenate(

        (dataX,tmp1.reshape((num_data,1)),tmp2.reshape((num_data,1)),tmp3.reshape((num_data,1))),axis=1)

    return new_dataX

if __name__=="__main__":

    cost_list=[]

    for i in range(1000):

        dataX,dataY=gen_data()

        wLIN=w_lin(dataX,dataY)

        cost_list.append(zero_one_cost(pred(dataX,wLIN),dataY))

    # show results

    print("the average Ein over 1000 experiments: ",sum(cost_list)/len(cost_list))

    plt.figure()

    plt.hist(cost_list)

    plt.xlabel("zero_one Ein")

    plt.ylabel("frequency")

    plt.title("13")

    plt.savefig("13.png")

    W=[]

    cost_list=[]

    for i in range(1000):

        # train

        dataX,dataY=gen_data()

        dataX=feat_transform(dataX)

        wLIN=w_lin(dataX,dataY)

        W.append(wLIN[:,0].tolist())

        # test

        testX, testY = gen_data()

        testX = feat_transform(testX)

        cost_list.append(zero_one_cost(pred(testX, wLIN), testY))

    min_cost=min(cost_list)

    min_id=cost_list.index(min_cost)

    print(W[min_id])

    W=np.array(W)

    # show w3

    print("the average w3 over 1000 experiments: ",np.average(W,axis=0)[3])

    plt.figure()

    plt.hist(W[:,3].tolist())

    plt.xlabel("w3")

    plt.ylabel("frequency")

    plt.title("14")

    plt.savefig("14.png")

    # show Eout

    print("the average Eout over 1000 experiments: ",sum(cost_list)/len(cost_list))

    plt.figure()

    plt.hist(cost_list)

    plt.xlabel("Eout")

    plt.ylabel("frequency")

    plt.title("15")

    plt.savefig("15.png")

18-20

# coding: utf-8

import numpy as np

def sigmoid(x):

    return 1/(1+np.e**(-x))

def read_data(dataFile):

    with open(dataFile,'r') as f:

        lines=f.readlines()

        data_list=[]

        for line in lines:

            line=line.strip().split()

            data_list.append([1.0] + [float(l) for l in line])

        dataArray=np.array(data_list)

        num_data=dataArray.shape[0]

        num_dim=dataArray.shape[1]-1

        dataX=dataArray[:,:-1].reshape((num_data,num_dim))

        dataY=dataArray[:,-1].reshape((num_data,1))

        return dataX,dataY

def gradient_descent(w,dataX,dataY,eta):

    assert w.shape[0]==dataX.shape[1],"wrong shape!"

    assert w.shape[1]==1,"wrong shape of w!"

    num_data=dataX.shape[0]

    num_dim=dataX.shape[1]

    tmp1=-dataY*dataX

    tmp2=-dataY*np.dot(dataX,w)

    for i in range(num_data):

        tmp2[i][0]=sigmoid(tmp2[i][0])

    tmp3=np.average(tmp1 * tmp2, axis=0)

    new_w=w-eta*tmp3.reshape((num_dim,1))

    return new_w

def s_gradient_descent(w,dataX,dataY,eta):

    assert w.shape[0]==dataX.shape[1],"wrong shape!"

    assert w.shape[1]==1,"wrong shape of w!"

    assert dataX.shape[0]==1,"wrong shape of x!"

    assert dataY.shape[0]==1,"wrong shape of y!"

    num_dim=dataX.shape[1]

    tmp1=-dataY*dataX

    tmp2=-dataY*np.dot(dataX,w)

    tmp2[0][0]=sigmoid(tmp2[0][0])

    tmp3=np.average(tmp1 * tmp2, axis=0)

    new_w=w-eta*tmp3.reshape((num_dim,1))

    return new_w

def pred(wLOG,dataX):

    pred=np.dot(dataX,wLOG)

    num_data=dataX.shape[0]

    for i in range(num_data):

        pred[i][0]=sigmoid(pred[i][0])

        if(pred[i][0]>=0.5):

            pred[i][0]=1

        else:

            pred[i][0]=-1

    return pred

def zero_one_cost(pred,dataY):

    return np.sum(pred!=dataY)/dataY.shape[0]

if __name__=="__main__":

    # train

    dataX,dataY=read_data("hw3_train.dat")

    num_dim=dataX.shape[1]

    w=np.zeros((num_dim,1))

    print("\n18")

    for i in range(2000):

        w=gradient_descent(w,dataX,dataY,eta=0.001)

    print("the weight vector within g: ",w[:,0])

    # test

    testX,testY=read_data("hw3_test.dat")

    Eout=zero_one_cost(pred(w,testX),testY)

    print("the Eout(g) on the test set: ",Eout)

    print("\n18.1")

    w = np.zeros((num_dim, 1))

    for i in range(20000):

        w = gradient_descent(w, dataX, dataY, eta=0.001)

    print("the weight vector within g: ", w[:, 0])

    # test

    Eout = zero_one_cost(pred(w, testX), testY)

    print("the Eout(g) on the test set: ", Eout)

    print("\n19")

    w=np.zeros((num_dim,1))

    for i in range(2000):

        w = gradient_descent(w, dataX, dataY, eta=0.01)

    print("the weight vector within g: ", w[:, 0])

    # test

    Eout = zero_one_cost(pred(w, testX), testY)

    print("the Eout(g) on the test set: ", Eout)

    print("\n20")

    w=np.zeros((num_dim,1))

    num_data=dataX.shape[0]

    for i in range(2000):

        i%=num_data

        x=dataX[i,:].reshape((1,num_dim))

        y=dataY[i,:].reshape((1,1))

        w=s_gradient_descent(w,x,y,eta=0.001)

    print("the weight vector within g: ", w[:, 0])

    # test

    Eout = zero_one_cost(pred(w, testX), testY)

    print("the Eout(g) on the test set: ", Eout)