Python 梯度下降实现逻辑回归

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

import os
path = ‘data‘+os.sep+‘LogiReg_data.txt‘ 
pdData = pd.read_csv(path,header = None,names = [‘Exam 1‘,‘Exam 2‘,‘Admitted‘])
#设置header值为None，然后指定header值为names
pdData.head()

positive = pdData[pdData[‘Admitted‘] == 1]
negative = pdData[pdData[‘Admitted‘] == 0]

fig,ax = plt.subplots(figsize=(10,5))
ax.scatter(positive[‘Exam 1‘],positive[‘Exam 2‘],s=30,c=‘b‘,marker=‘o‘,label=‘Admitted‘)
ax.scatter(negative[‘Exam 1‘],negative[‘Exam 2‘],s=30,c=‘r‘,marker=‘x‘,label=‘Not Admitted‘)
ax.legend()
ax.set_xlabel(‘Exam 1 Score‘)
ax.set_ylabel(‘Exam 2 Score‘)
fig

def sigmod(z):
    return 1/(1+np.exp(-z))

def model(X,theta):
    return sigmod(np.dot(X,theta.T))

pdData.insert(0,‘ones‘,1)

original_data = pdData.as_matrix()
cols = original_data.shape[1]       #cols记录一共有几列数据
X = original_data[:,0:cols-1]       
Y = original_data[:,cols-1:cols]

theta = np.zeros([1,3])             #theta = array([[0., 0., 0.]]),构造全为零的行向量

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))

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])             #(h(Xi)-Yi)*Xi
        grad[0,j] = np.sum(term)/len(X)              #∑term / m
    return grad

STOP_ITER = 0
STOP_COST = 1
STOP_GRAD = 2

def stop_fun(type,value,threshold):
    if type == STOP_ITER:  
        return value > threshold                              #达到一定次数后停止
    elif type == STOP_COST:
        return abs(value[-1]-value[-2]) < threshold           #小于一定阈值时停止
    elif type == STOP_GRAD:      
        return np.linalg.norm(value) < threshold              #小于一定阈值时停止 

import numpy.random

def shuffleData(data):
    np.random.shuffle(data)           #将数据打乱
    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):
    init_time = time.time()
    i = 0     #迭代次数
    k = 0     #batch
    X,Y = shuffleData(data)
    grad = np.zeros(theta.shape)      #梯度初始化
    costs = [cost(X,Y,theta)]          #计算损失值
    
    while 1:
        grad = gradient(X[k:k+batchSize],Y[k:k+batchSize],theta)
        k+=batchSize
        if k >= n:
            k = 0
            X,Y = shuffleData(data)
        theta = theta - alpha*grad                   #对参数进行更新
        costs.append(cost(X,Y,theta))
        i += 1
            
        if stopType == STOP_ITER:  
            value = i
        elif stopType == STOP_COST:
            value = costs
        elif stopType == STOP_GRAD:
            value = grad
        if stop_fun(stopType,value,thresh): break
            
    return theta,i-1,costs,grad,time.time()-init_time

def run_example(data, theta, batchSize, stopType, thresh, alpha):
    theta,iter,costs,grad,times = descent(data,theta,batchSize,stopType,thresh,alpha)
    
    name = ‘Original‘ 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 + " descent - Stop: "            #输出梯度下降策略
    if stopType == STOP_ITER:
        strStop = "{} iterations".format(thresh)
    elif stopType == STOP_COST: 
        strStop = "costs change < {}".format(thresh)
    else: 
        strStop = "gradient norm < {}".format(thresh)
    name += strStop                                      #输出停止策略
    print ("***{}\nTheta: {} - Iter: {} - Last cost: {:03.2f} - Duration: {:03.2f}s".format(name, theta, iter, costs[-1], times))    
    #打印相关信息
    
    #画图
    fig,ax = plt.subplots(figsize = (12,4))
    ax.plot(np.arange(len(costs)),costs,‘r‘)
    ax.set_xlabel(‘Iterations‘)
    ax.set_ylabel(‘Cost‘)
    ax.set_title(name.upper() + ‘ - Error vs. Iteration‘)
    plt.show(fig)
    return theta

from sklearn import preprocessing as pp

scaled_data = original_data.copy()
scaled_data[:,1:3] = pp.scale(original_data[:,1:3])

run_example(scaled_data, theta, n, STOP_ITER, thresh=5000, alpha=0.001)

theta = run_example(scaled_data, theta, 1, STOP_GRAD, thresh=0.002/5, alpha=0.001)

def predict(X,theta):
    return [1 if x>= 0.5 else 0 for x in model(X,theta)]

scaled_X = scaled_data[:,:3]
scaled_Y = scaled_data[:,3]
predictions = predict(scaled_X,theta)
correct = [1 if((a==1 and b==1) or (a==0 and b==0)) else 0 for (a,b) in zip(predictions,scaled_Y)]
accuracy = (sum(map(int,correct)) % len(correct))
print(‘accuracy = {0}%‘.format(accuracy))

from sklearn.cross_validation import KFold
from sklearn.cross_validation import cross_val_score
from sklearn.linear_model import LogisticRegression

kf = KFold(len(scaled_X),10,shuffle = True,random_state = 8)
lr = LogisticRegression()
accuracies = cross_val_score(lr,scaled_X,scaled_Y,scoring = ‘roc_auc‘,cv=kf)
average_accuracy = sum(accuracies)/len(accuracies)
plot_roc(scaled_Y,predictions)

print(accuracies)
print(average_accuracy)

from sklearn.metrics import roc_curve, auc

def plot_roc(labels, predict_prob):
    #labels:正确标签
    #predict_prob:预测标签
    false_positive_rate,true_positive_rate,thresholds=roc_curve(labels, predict_prob)
    roc_auc=auc(false_positive_rate, true_positive_rate)
    plt.title(‘ROC‘)
    plt.plot(false_positive_rate, true_positive_rate,‘b‘,label=‘AUC = %0.4f‘% roc_auc)
    plt.legend(loc=‘lower right‘)
    plt.plot([0,1],[0,1],‘r--‘)
    plt.ylabel(‘TPR‘)
    plt.xlabel(‘FPR‘)
    plt.show()