逻辑回归算法实现

程序员文章站 2022-04-28 11:59:10

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逻辑回归算法原理还是比较容易理解的，根据计算的结果实现一下：

手写的推导过程如下：

逻辑回归算法实现

然后我们开始写实现的过程

1、写出判断模型准确性的函数，这个比较容易理解

import numpy as np
from math import sqrt


def accuracy_score(y_true, y_predict):
    """计算y_true和y_predict之间的准确率"""
    assert len(y_true) == len(y_predict), \
        "the size of y_true must be equal to the size of y_predict"

    return np.sum(y_true == y_predict) / len(y_true)

2、写出来训练数据集和测试数据集的分割函数，这个也可以直接用sklearn中写好的包

import numpy as np


def train_test_split(X, y, test_ratio=0.2, seed=None):
    """将数据 X 和 y 按照test_ratio分割成X_train, X_test, y_train, y_test"""
    assert X.shape[0] == y.shape[0], \
        "the size of X must be equal to the size of y"
    assert 0.0 <= test_ratio <= 1.0, \
        "test_ration must be valid"

    if seed:
        np.random.seed(seed)

    shuffled_indexes = np.random.permutation(len(X))

    test_size = int(len(X) * test_ratio)
    test_indexes = shuffled_indexes[:test_size]
    train_indexes = shuffled_indexes[test_size:]

    X_train = X[train_indexes]
    y_train = y[train_indexes]

    X_test = X[test_indexes]
    y_test = y[test_indexes]

    return X_train, X_test, y_train, y_test

3、写出函数的fit过程，求解用的是批量梯度下降法，这个过程和线性回归比较类似

import numpy as np

class LogisticRegression:

    def __init__(self):
        """初始化模型"""
        self.coef_ = None
        self.intercept_ = None
        self._theta = None


    #有下划线是私有函数
    def _sigmod(self,t):
        return 1./(1.+np.exp(-t))

    def fit(self,X_train,y_train,eta=0.01,n_iters=1e4):
        """根据模型训练数据集X_train,y_train,使用梯度下降法训练Logistic Regression"""
        assert X_train.shape[0] == y_train.shape[0],\
            "the size of X_train must be equal to the size of y_trian"

        #计算损失函数
        def J(theta,X_b,y):
            y_hat = self._sigmod(X_b.dot(theta))
            try:
                return -np.sum(y*np.log(y_hat) + (1-y)*np.log(1-y_hat))/ len(y)
            except:
                return float("inf")

        def dJ(theta,X_b,y):
            return X_b.T.dot(self._sigmod(X_b.dot(theta))-y) / len(X_b)

        def gradient_descent(X_b, y, inital_theta, eta, n_inters=1e4, epsilon=1e-8):
            theta = initial_theta
            i_inter = 0

            while i_inter < n_inters:
                gradient = dJ(theta, X_b, y)
                last_theta = theta
                theta = theta - eta * gradient

                if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):
                    break

                i_inter += 1
            return theta

        X_b = np.hstack([np.ones((len(X_train),1)),X_train])
        initial_theta = np.zeros(X_b.shape[1])
        self._theta = gradient_descent(X_b,y_train,initial_theta,eta,n_iters)

        self.intercept_ = self._theta[0]
        self.coef_ = self._theta[1:]

        return self

4、写出来预测的概率和预测的分类结果

    #预测的概率函数
    def predict_proba(self,X_predict):
        """给定待预测数据集X_predict,返回X_predict的结果向量"""
        assert self.intercept_ is not None and self.coef_ is not None,\
            "Must fit before predixt"
        assert X_predict.shape[1] == len(self.coef_),\
            "the feature number of X_predict must be equal to X_train"

        X_b = np.hstack([np.ones((len(X_predict),1)), X_predict])
        return  self._sigmod(X_b.dot(self._theta))

    #预测结果的函数
    def predict(self,X_predict):
        """给定预测数据集X_predict,返回表示X_predict的结果向量"""
        assert self.intercept_ is not None and self.coef_ is not None,\
            "Must fit before predixt"
        assert X_predict.shape[1] == len(self.coef_),\
            "the feature number of X_predict must be equal to X_train"

        proba = self.predict_proba(X_predict)
        return np.array(proba >= 0.5, dtype='int')
    def score(self, X_test, y_test):
        """根据测试数据集X_test和y_test确定当前模型的准确度"""

        y_predict = self.predict(X_test)
        return accuracy_score(y_test,y_predict)

    def __repr__(self):
        return  "LogisticRegression()"

5、然后用iris数据集验证下我们写的函数

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.model_selection import train_test_split

iris = datasets.load_iris()
X = iris.data
y = iris.target

X = X[y<2, :2]
y = y[y<2]

plt.scatter(X[y ==0,0],X[y==0,1],color='red')
plt.scatter(X[y ==1,0],X[y==1,1],color='blue')
plt.show()


X_train,X_test,y_train,y_test = train_test_split(X,y)

log_reg = LogisticRegression()
log_reg.fit(X_train,y_train)


log_reg.score(X_test,y_test)

结果如下：

逻辑回归算法实现