建立一个逻辑回归模型来预测一个学生是否被大学录取。假设你是一个大学管理员，你想根据两次考试的结果 来决定每个申请人的录取机会，你有以前申请人的历史数据，你可以用它作为逻辑回归的训练集。对于每一个培训 例子，有两个考试的申请人的分数和录取决定，为了做到这一点，建立一个分类模型，根据考试成绩估计入学概率。
导入数据，并读取数据
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
pdData=pd.read_csv("LogiReg_data.txt",header=None,names=['Exam1','Exam2','Admitted'])
print(pdData.head())
画图：
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
pdData=pd.read_csv("LogiReg_data.txt",header=None,names=['Exam1','Exam2','Admitted'])
# print(pdData.head())
# print(pdData.shape)
#画图
positive=pdData[pdData["Admitted"]==1]
negative=pdData[pdData["Admitted"]==0]
fig,ax=plt.subplots(figsize=(10,5))#指定画图域
#散点图
ax.scatter(positive['Exam1'],positive["Exam2"],s=30,c='b',marker='o',label="Admitted")
ax.scatter(negative['Exam1'],negative["Exam2"],s=30,c='r',marker='x',label="Not Admitted")
ax.legend()
ax.set_xlabel("Exam1 Score")
ax.set_ylabel("Exam2 Score")
plt.show()
The logistic regression
目标：建立分类器（求解出三个参数Θ0，Θ1，Θ2）
设定阈值，根据阈值判断录取结果
要完成的模块：
- sigmoid:映射到概率的函数
- model：返回预测结果值
- cost：根据参数计算损失
- gradient：计算每个参数的梯度方向
- descent：进行参数更新
- accuracy：计算精度
sigmoid函数：
def sigmoid(z):
return 1/(1+np.exp(-z))损失函数
#预测函数
def model(X,theta):
return sigmoid(np.dot(X,theta.T))
pdData.insert(0,"Ones",1)#加入一列
orig_data=pdData.as_matrix()
cols=orig_data.shape[1]
X=orig_data[:,0:cols-1]
y=orig_data[:,cols-1:cols]
theta=np.zeros([1,3])
#print(X)
#print(y)
#print(theta)
def cost(X,y,theta):
left=np.multiply(-y,np.log(model(X,theta)))
right=np.multiply(1-y,np.log(1-model(X,theta)))
return np.sum(left-right)/len(X)
计算梯度：
def gradient(X,y,theta):
grad=np.zeros(theta.shape)
error=(model(X,theta)-y).ravel()
for i in range(len(theta.ravel())):
term=np.multiply(error,X[:,j])
grad[0,j]=np.sum(term)/len(X)
return gradGradient descent
比较3种不同梯度下降方法：
#完整代码：
"""
建立一个逻辑回归模型来预测一个学生是否被大学录取。假设你是一个大学管理员，你想根据两次考试的结果
来决定每个申请人的录取机会，你有以前申请人的历史数据，你可以用它作为逻辑回归的训练集。对于每一个培训
例子，有两个考试的申请人的分数和录取决定，为了做到这一点，建立一个分类模型，根据考试成绩估计入学概率
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
pdData=pd.read_csv("LogiReg_data.txt",header=None,names=['Exam1','Exam2','Admitted'])
# print(pdData.head())
# print(pdData.shape)
#画图
positive=pdData[pdData["Admitted"]==1]
negative=pdData[pdData["Admitted"]==0]
fig,ax=plt.subplots(figsize=(10,5))#指定画图域
#散点图
ax.scatter(positive['Exam1'],positive["Exam2"],s=30,c='b',marker='o',label="Admitted")
ax.scatter(negative['Exam1'],negative["Exam2"],s=30,c='r',marker='x',label="Not Admitted")
ax.legend()
ax.set_xlabel("Exam1 Score")
ax.set_ylabel("Exam2 Score")
#plt.show()
def sigmoid(z):
return 1/(1+np.exp(-z))
#预测函数
def model(X,theta):
return sigmoid(np.dot(X,theta.T))
pdData.insert(0,"Ones",1)#加入一列
orig_data=pdData.as_matrix()
cols=orig_data.shape[1]
X=orig_data[:,0:cols-1]
y=orig_data[:,cols-1:cols]
theta=np.zeros([1,3])
#print(X)
#print(y)
#print(theta)
def cost(X,y,theta):
left=np.multiply(-y,np.log(model(X,theta)))
right=np.multiply(1-y,np.log(1-model(X,theta)))
return np.sum(left-right)/len(X)
print(cost(X,y,theta))
def gradient(X,y,theta):
grad=np.zeros(theta.shape)
error=(model(X,theta)-y).ravel()
for j in range(len(theta.ravel())):
term=np.multiply(error,X[:,j])
grad[0,j]=np.sum(term)/len(X)
return grad
STOP_ITER=0#根据迭代次数停止
STOP_COST=1#根据迭代损失停止
STOP_GRAD=2#根据梯度
def stopCriterion(type,value,threshold):
#设定三种不同停止策略
if type==STOP_ITER:
return value>threshold
elif type==STOP_COST:
return abs(value[-1]-value[-2])<threshold
elif type==STOP_GRAD:
return np.linalg.norm(value)<threshold
import numpy.random
#洗牌，打乱数据顺序
def shuffleData(data):
np.random.shuffle(data)
cols=data.shape[1]
X=data[:,0:cols-1]
y=data[:,cols-1:]
return X,y
import time
def descent(data,theta,batchSize,stopType,thresh,alpha):
#梯度下降求解
init_time=time.time()
i=0#迭代次数
k=0#batch
X,y=shuffleData(data)
grad=np.zeros(theta.shape)#计算的梯度
costs=[cost(X,y,theta)]#损失值
while True:
grad=gradient(X[k:k+batchSize],y[k:k+batchSize],theta)
k+=batchSize#取batch数量个数据
if k>=n:
k=0
X,y=shuffleData(data)#重新洗牌
theta=theta-alpha*grad#参数更新
costs.append(cost(X,y,theta))#计算新的损失
i+=1
if stopType==STOP_ITER:
value=1
elif stopType==STOP_COST:
value=costs
elif stopType==STOP_GRAD:
value=grad
if stopCriterion(stopType,value,thresh):
break
return theta,i-1,costs,grad,time.time()-init_time
def runExpe(data,theta,batchSize,stopType,thresh,alpha):
theta,iter,costs,grad,dur=descent(data,theta,batchSize,stopType,thresh,alpha
)
name="Orignal" if(data[:,1]>2).sum()>1 else "Scaled"
name+= " data - learning rate:{}=".format(alpha)
if batchSize==n:strDescType="Gradient"
elif batchSize==1:strDescType="Stochastic"
else:strDescType="Mini-batch({})".format(batchSize)
name+=strDescType+" desent - Stop:"
if stopType ==STOP_ITER:strStop="{}iterations".format(thresh)
elif stopType==stopType==STOP_COST:strStop="costs change<{}".format(thresh)
else:strStop="gradient norm<{}".format(thresh)
name+=strStop
print('***{}\nTheta:{}-Iter:{}-Last cost{:03.2f}-Duration :{:03.2f}s'.format(name,theta,iter,costs[-1],dur))
fig,ax=plt.subplots(figsize=(12,4))
ax.plot(np.arange(len(costs)),costs,'r')
ax.set_xlabel("Iterations")
ax.set_ylabel("Costs")
ax.set_title(name.upper()+' -Error vs:Iteration')
return theta
n=100
runExpe(orig_data,theta,n,STOP_ITER,thresh=5000,alpha=0.000001)LogiReg_data.txt
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