机器学习基石笔记:Homework #2 decision stump相关习题
原文地址:http://www.jianshu.com/p/4bc01760ac20
问题描述
程序实现
17-18
# coding: utf-8
import numpy as np
import matplotlib.pyplot as plt
def sign(n):
if(n>0):
return 1
else:
return -1
def gen_data():
data_X=np.random.uniform(-1,1,(20,1))# [-1,1)
data_Y=np.zeros((20,1))
idArray=np.random.permutation([i for i in range(20)])
for i in range(20):
if(i<20*0.2):
data_Y[idArray[i]][0]=-sign(data_X[idArray[i]][0])
else:
data_Y[idArray[i]][0] = sign(data_X[idArray[i]][0])
data=np.concatenate((data_X,data_Y),axis=1)
return data
def decision_stump(dataArray):
minErrors=20
min_s_theta_list=[]
num_data=dataArray.shape[0]
data=dataArray.tolist()
data.sort(key=lambda x:x[0])
for s in [-1.0,1.0]:
for i in range(num_data):
if(i==num_data-1):
theta=(data[i][0]+1.0)/2
else:
theta=(data[i][0]+data[i+1][0])/2
errors=0
for i in range(20):
pred=s*sign(data[i][0]-theta)
if(pred!=data[i][1]):
errors+=1
if(minErrors>errors):
minErrors=errors
min_s_theta_list=[]
elif(minErrors<errors):
continue
min_s_theta_list.append((s, theta))
i=np.random.randint(low=0,high=len(min_s_theta_list))
min_s,min_theta=min_s_theta_list[i]
return minErrors,min_s,min_theta
def computeEinEout(minErrors,min_s,min_theta):
Ein=minErrors/20
Eout=0.5+0.3*min_s*(abs(min_theta)-1)
return Ein,Eout
if __name__=="__main__":
Ein_list=[]
Eout_list=[]
for i in range(5000):
dataArray=gen_data()
minErrors,min_s,min_theta=decision_stump(dataArray)
Ein,Eout=computeEinEout(minErrors,min_s,min_theta)
Ein_list.append(Ein)
Eout_list.append(Eout)
# show results
# 17 & 18
print("the average Ein: ",sum(Ein_list)/5000)
print("the average Eout: ",sum(Eout_list)/5000)
plt.figure(figsize=(16,6))
plt.subplot(121)
plt.hist(Ein_list)
plt.xlabel("Ein")
plt.ylabel("frequency")
plt.subplot(122)
plt.hist(Eout_list)
plt.xlabel("Eout")
plt.ylabel("frequency")
plt.savefig("EinEout.png")
19-20
# coding: utf-8
import numpy as np
def read_data(dataFile):
with open(dataFile, 'r') as file:
data_list = []
for line in file.readlines():
line = line.strip().split()
data_list.append([float(l) for l in line])
data_array = np.array(data_list)
return data_array
def predict(s,theta,dataX):
num_data=dataX.shape[0]
res=s*np.sign(dataX-theta)
return res
def decision_stump(dataArray):
min_s_theta_list=[]
num_data=dataArray.shape[0]
minErrors=num_data
data=dataArray.tolist()
data.sort(key=lambda x:x[0])
dataArray=np.array(data)
dataX=dataArray[:,0].reshape(num_data,1)
dataY=dataArray[:,1].reshape(num_data,1)
for s in [-1.0,1.0]:
for i in range(num_data):
if(i==num_data-1):
theta=(dataX[i][0]*2+1)/2
else:
theta=(dataX[i][0]+dataX[i+1][0])/2
pred=predict(s,theta,dataX)
errors=np.sum(pred!=dataY)
if(minErrors>errors):
minErrors=errors
min_s_theta_list=[]
elif(minErrors<errors):
continue
min_s_theta_list.append((s, theta))
i=np.random.randint(low=0,high=len(min_s_theta_list))
min_s,min_theta=min_s_theta_list[i]
return minErrors,min_s,min_theta
def best_of_best(candidate):
candidate.sort(key=lambda x:x[1])
counts=0
for i in range(len(candidate)):
if(candidate[i][1]!=candidate[0][1]):
break
counts+=1
i=np.random.randint(low=0,high=counts)
return candidate[i][0],candidate[i][1],candidate[i][2],candidate[i][3]
if __name__=="__main__":
data_array=read_data("hw2_train.dat")
num_data=data_array.shape[0]
num_dim=data_array.shape[1]-1
candidate=[]
dataY=data_array[:,-1].reshape(num_data,1)
for i in range(num_dim):
dataX=data_array[:,i].reshape(num_data,1)
min_errors,min_s,min_theta=decision_stump(np.concatenate((dataX,dataY),axis=1))
candidate.append([i,min_errors,min_s,min_theta])
min_id,min_errors,min_s,min_theta=best_of_best(candidate)
print("the optimal decision stump:\n","s: ",min_s,"\ntheta: ",min_theta)
print("the Ein of the optimal decision stump:\n",min_errors/num_data)
test_array=read_data("hw2_test.dat")
num_test=test_array.shape[0]
testY=test_array[:,-1].reshape(num_test,1)
num_dim=test_array.shape[1]-1
testX=test_array[:,min_id].reshape(num_test,1)
pred=predict(min_s,min_theta,testX)
print("the Eout of the optimal decision stump by Etest:\n",np.sum(pred!=testY)/num_test)
运行结果
17-18
19-20
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