李航《统计学习方法》——第六章 逻辑斯谛回归模型

由于网上资料很多，这里就不再对算法原理进行推导，仅给出博主用Python实现的代码，供大家参考

二项逻辑斯谛回归

适用问题：二类分类

可类比于感知机算法

实验数据：train_binary.csv

实现代码：

# encoding=utf-8

import time
import math
import random
import pandas as pd

from sklearn.cross_validation import train_test_split
from sklearn.metrics import accuracy_score


class LogisticRegression(object):

    def __init__(self):
        self.learning_step = 0.0001 # 学习率
        self.max_iteration = 5000 # 分类正确上界，当分类正确的次数超过上界时，认为已训练好，退出训练

    def train(self,features, labels):
        self.w = [0.0] * (len(features[0]) + 1) # 初始化模型参数

        correct_count = 0 # 分类正确的次数

        while correct_count < self.max_iteration:

            # 随机选取数据(xi,yi)
            index = random.randint(0, len(labels) - 1)
            x = list(features[index])
            x.append(1.0)
            y = labels[index]

            if y == self.predict_(x): # 分类正确的次数加1,并跳过下面的步骤
                correct_count += 1
                continue

            wx = sum([self.w[i] * x[i] for i in range(len(self.w))])
            while wx>700: # 控制运算结果越界
                wx/=2
            exp_wx = math.exp(wx)

            for i in range(len(self.w)):
                self.w[i] -= self.learning_step * \
                    (-y * x[i] + float(x[i] * exp_wx) / float(1 + exp_wx))

    def predict_(self,x):
        wx = sum([self.w[j] * x[j] for j in range(len(self.w))])
        while wx>700: # 控制运算结果越界
            wx/=2
        exp_wx = math.exp(wx)

        predict1 = exp_wx / (1 + exp_wx)
        predict0 = 1 / (1 + exp_wx)

        if predict1 > predict0:
            return 1
        else:
            return 0


    def predict(self,features):
        labels = []

        for feature in features:
            x = list(feature)
            x.append(1)
            labels.append(self.predict_(x))

        return labels

if __name__ == "__main__":
    print("Start read data...")

    time_1 = time.time()

    raw_data = pd.read_csv('../data/train_binary.csv', header=0)  # 读取csv数据，并将第一行视为表头，返回DataFrame类型
    data = raw_data.values

    features = data[::, 1::]
    labels = data[::, 0]

    # 避免过拟合，采用交叉验证，随机选取33%数据作为测试集，剩余为训练集
    train_features, test_features, train_labels, test_labels = train_test_split(features, labels, test_size=0.33, random_state=0)

    time_2 = time.time()
    print('read data cost %f seconds' % (time_2 - time_1))

    print('Start training...')
    lr = LogisticRegression()
    lr.train(train_features, train_labels)
    time_3 = time.time()
    print('training cost %f seconds' % (time_3 - time_2))

    print('Start predicting...')
    test_predict = lr.predict(test_features)
    time_4 = time.time()
    print('predicting cost %f seconds' % (time_4 - time_3))

    score = accuracy_score(test_labels, test_predict)
print("The accruacy score is %f" % score)

代码可从这里logistic_regression/logistic_regression.py获得

运行结果：

(多项)逻辑斯谛回归

适用问题：多类分类

实验数据：train.csv

实现代码(用sklearn实现)：

# encoding=utf-8

import pandas as pd
import time

from sklearn.cross_validation import train_test_split
from sklearn.metrics import accuracy_score

from sklearn.linear_model import LogisticRegression



if __name__ == '__main__':

    print("Start read data...")
    time_1 = time.time()

    raw_data = pd.read_csv('../data/train.csv', header=0) 
    data = raw_data.values

    features = data[::, 1::]
    labels = data[::, 0]

    # 随机选取33%数据作为测试集，剩余为训练集
    train_features, test_features, train_labels, test_labels = train_test_split(features, labels, test_size=0.33, random_state=0)

    time_2 = time.time()
    print('read data cost %f seconds' % (time_2 - time_1))


    print('Start training...') 
    # multi_class可选‘ovr’, ‘multinomial’，默认为ovr用于二类分类，multinomial用于多类分类
    clf = LogisticRegression(max_iter=100,solver='saga',multi_class='multinomial')
    clf.fit(train_features,train_labels)
    time_3 = time.time()
    print('training cost %f seconds' % (time_3 - time_2))


    print('Start predicting...')
    test_predict = clf.predict(test_features)
    time_4 = time.time()
    print('predicting cost %f seconds' % (time_4 - time_3))


    score = accuracy_score(test_labels, test_predict)
print("The accruacy score is %f" % score)

代码可从这里logistic_regression/logistic_regression_sklearn.py获得

运行结果：