手写逻辑回归代码

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

导入相关数据并进行简单的数据处理

os.chdir('D:\\proj\\titanic')
df=pd.read_csv('train.csv',encoding='gbk')
df.columns
sex_dummy=pd.get_dummies(df['Sex'],prefix='Sex')
pclass_dummy=pd.get_dummies(df['Pclass'],prefix='Pclass')
embarked_dummy=pd.get_dummies(df['Embarked'],prefix='Embarked')
parch_dummy=pd.get_dummies(df['Parch'],prefix='Parch')
sibsp_dummy=pd.get_dummies(df['SibSp'],prefix='SibSp')
df.drop(['PassengerId','Sex','Pclass','Embarked','Parch','SibSp','Name','Ticket','Cabin'],axis=1,inplace=True)
df_train=pd.concat([df,sex_dummy,pclass_dummy,embarked_dummy,parch_dummy,sibsp_dummy],axis=1)
dataset=df_train.reindex(columns=['Age','Fare', 'Sex_female', 'Sex_male', 'Pclass_1','Pclass_2', 'Pclass_3', 'Embarked_C', 'Embarked_Q', 'Embarked_S','Parch_0', 'Parch_1', 'Parch_2', 'Parch_3', 'Parch_4', 'Parch_5', 'Parch_6', 'SibSp_0', 'SibSp_1', 'SibSp_2', 'SibSp_3', 'SibSp_4', 'SibSp_5', 'SibSp_8','Survived' ])
dataset_1=df_train.reindex(columns=['Fare', 'Sex_female', 'Sex_male', 'Pclass_1','Pclass_2', 'Pclass_3', 'Embarked_C', 'Embarked_Q', 'Embarked_S','Parch_0', 'Parch_1', 'Parch_2', 'Parch_3', 'Parch_4', 'Parch_5', 'Parch_6', 'SibSp_0', 'SibSp_1', 'SibSp_2', 'SibSp_3', 'SibSp_4', 'SibSp_5', 'SibSp_8','Survived' ])
dataset['Age'].fillna(np.mean(dataset['Age']),inplace=True)
dataset.info()

开始手写代码

逻辑回归函数

#逻辑回归函数
def sigmoid(x):
    s=1/(1+np.exp(-x))
    return s

定义标准化函数

#将xmat标准化
def normalizer(xmat):
    inmat=xmat.copy()
    mean=np.mean(inmat,axis=0)
    std=np.std(inmat,axis=0)
    result=(inmat-mean)/std
    return result

计算损失函数

#计算损失函数
def Loss(xmat,ymat,weight,n):
    y_pred=sigmoid(xmat*weight)
    loss=-(1/n)*np.sum((np.multiply(ymat,np.log(y_pred))+np.multiply((1-ymat),np.log(1-y_pred))))
    return loss

计算逻辑回归权重

#计算逻辑回归的权重
def BDG_LR(dataset,penalty=None,Lambda=1,alpha=0.001,mat_iter=10001):
    xmat=np.mat(dataset.iloc[:,:-1])
    ymat=np.mat(dataset.iloc[:,-1]).reshape(-1,1)
    xmat=normalizer(xmat)
    n,m=xmat.shape
    losslist=[]
    weight=np.zeros((m,1))
    for i in range(mat_iter):
        grad=xmat.T*(sigmoid(xmat*weight)-ymat)/n
        # print((sigmoid(xmat*weight)-ymat))
        # print(grad)
        if penalty=='l2':
            grad=grad+Lambda*weight
        if penalty=='l1':
            grad=grad+Lambda*np.sign(weight)
        weight=weight-alpha*grad
        if i % 100 ==0:
            losslist.append(Loss(xmat,ymat,weight,n))
    #随着迭代次数的增加，用新的权重计算损失函数
    plt.figure()
    x=range(len(losslist))
    plt.plot(x,losslist,color='r')
    plt.xlabel('number')
    plt.ylabel('loss')
    plt.show()
    return weight,losslist

用数据集测试

BDG_LR(dataset,penalty='l2')

损失函数结果如下图