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前言

最近准备开始学习机器学习，后续将对学习内容进行记录，该文主要针对逻辑回归代码实现进行记录！

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一、逻辑回归是什么？

逻辑回归概念篇可看博主之前的文章，传送门

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二、代码实现

1.数据说明

你想根据两次考试的结果来决定每个申请人的录取机会。你有以前的申请人的历史数据，你可以用它作为逻辑回归的训练集。对于每一个培训例子，你有两个考试的申请人的分数和录取决定。为了做到这一点，我们将建立一个分类模型，根据考试成绩估计入学概率。
数据源下载：数据下载 提取码: 5mf2

打开数据后可以看到，只有数字没有列名，于是在利用pandas创建DataFrame结构时需要手动指定header
数据导入

#三大件
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline   
# 可以在Ipython编译器里直接使用，功能是可以内嵌绘图，并且可以省略掉plt.show()这一步
import os
path = 'data' + os.sep + 'LogiReg_data.txt' #改成数据源路径
pdData = pd.read_csv(path, header=None, names=['Exam 1', 'Exam 2', 'Admitted'])#手动指定header
pdData.head()

输出为：

将数据用散点图绘制出来

positive = pdData[pdData['Admitted'] == 1] # returns the subset of rows such Admitted = 1, i.e. the set of *positive* examples
negative = pdData[pdData['Admitted'] == 0] # returns the subset of rows such Admitted = 0, i.e. the set of *negative* examplesfig, 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')

输出为

2.逻辑回归代码

目标：建立分类器（求解出三个参数 ${\theta }_0{\theta }_1{\theta }_2$）设定阈值，根据阈值判断录取结果(一般设置为0.5)
待完成模块：
·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

具体代码说明：
①sigmoid函数

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

②model函数

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

③增加一列取值为1的特征

if 'Ones' not in pdData.columns:pdData.insert(0, 'Ones', 1) # in a try / except structure so as not to return an error if the block si executed several times

④将pandas转换为ndarray，获取数据总列数

orig_data = pdData.values # convert the Pandas representation of the data to an array useful for further computations
cols = orig_data.shape[1]

⑤提取特征数据X，结果数据y，定义$\theta$

X = orig_data[:,0:cols-1]
y = orig_data[:,cols-1:cols]
theta = np.zeros([1, 3])

⑥损失函数
$J(\theta )=\frac{1}{n}{\sum }_{i=1}^n[(-ylog(h_{\theta }(x)))-(1-y)log(1-h_{\theta }(x))]$

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)) #n取决于传递进来的X样本的个数，根据不同的梯度下降方法对应不同的n

⑦计算梯度方向

def gradient(X, y, theta):grad = np.zeros(theta.shape)error = (model(X, theta)-y ).ravel() #拉成一个一维数组#有三个待求参数，需要对每个参数机进行求偏导后存放到grad数组中for j in range(len(theta.ravel())): #for each parmeterterm = np.multiply(error, X[:,j]) #相当于乘了每个样本的第j个特征grad[0, j] = np.sum(term) / len(X) #n取决于传递进来的X样本的个数，根据不同的梯度下降方法对应不同的nreturn grad #返回每一个参数应该下降

⑧比较3中不同梯度下降方法

STOP_ITER = 0#根据迭代次数停止
STOP_COST = 1#根据损失停止
STOP_GRAD = 2#根据梯度def stopCriterion(type, value, threshold):#设定三种不同的停止策略if type == STOP_ITER:        return value > thresholdelif type == STOP_COST:      return abs(value[-1]-value[-2]) < thresholdelif type == STOP_GRAD:      return np.linalg.norm(value) < thresholdimport numpy.random
#洗牌
def shuffleData(data):np.random.shuffle(data)cols = data.shape[1]X = data[:, 0:cols-1]y = data[:, cols-1:]return X, yimport time
#batchsize=1表示随机梯度下降，batchsize=100表示批量梯度下降，为其他表示小批量
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 # batchX, 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 = ielif stopType == STOP_COST:     value = costselif stopType == STOP_GRAD:     value = gradif stopCriterion(stopType, value, thresh): breakreturn theta, i-1, costs, grad, time.time() - init_timedef runExpe(data, theta, batchSize, stopType, thresh, alpha):#import pdb; pdb.set_trace();theta, iter, costs, grad, dur = 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: "if stopType == STOP_ITER: strStop = "{} iterations".format(thresh)elif stopType == STOP_COST: strStop = "costs change < {}".format(thresh)else: strStop = "gradient norm < {}".format(thresh)name += strStopprint ("***{}\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('Cost')ax.set_title(name.upper() + ' - Error vs. Iteration')return theta

对结果进行绘图分析：

#选择的梯度下降方法是基于所有样本的，迭代50000次，每一次步长为0.000001
n=100
runExpe(orig_data, theta, n, STOP_ITER, thresh=5000, alpha=0.000001)

runExpe(orig_data, theta, n, STOP_COST, thresh=0.000001, alpha=0.001)

runExpe(orig_data, theta, n, STOP_GRAD, thresh=0.05, alpha=0.001)

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