实现逻辑回归算法

  上一篇博客提出了逻辑回归的损失函数只能通过梯度下降法来求出，这里就不详细介绍具体的推导过程了，有兴趣的小伙伴可以自行查阅相关资料。这里我直接给出最后推导出的梯度的式子：

下面我们就具体编程实现逻辑回归。

# LogisticRegression.py

import numpy as np
from metrics import accuracy_score

class LogisticRegression:
    def __init__(self):
        """初始化 Linear Regression"""
        self.coef_ = None           # 系数
        self.interception_ = None   # 截距
        self._theta = None          # θ
    def _sigmoid(self, t):
        return 1. / (1. + np.exp(-t))
    def fit(self, X_train, y_train, eta=0.01, n_iters=1e4):
        """根据训练数据集X_train，y_train，使用梯度下降法训练Logistic Regression模型"""
        assert X_train.shape[0] == y_train.shape[0], \
            "the size of X_train, y_train must be equal to the size of y_train"
        def J(theta, X_b, y):
            y_hat = self._sigmoid(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._sigmoid(X_b.dot(theta)) - y)  / len(X_b)
        def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8):
            theta = initial_theta
            i_iter = 0
            while i_iter < n_iters:
                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_iter += 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)

        self.interception_ = self._theta[0]
        self.coef_ = self._theta[1:]
        return self
    def predict_proba(self, X_predict):
        """给定待预测数据集X_predict，返回表示X_predict的结果概率向量"""
        assert self.interception_ is not None and self.coef_ is not None, \
            "must fit before predict!"
        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._sigmoid(X_b.dot(self._theta))
    def predict(self, X_predict):
        """给定待预测数据集X_predict，返回表示X_predict的结果向量"""
        assert self.interception_ is not None and self.coef_ is not None, \
            "must fit before predict!"
        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()"

  具体代码见 52 实现逻辑回归.ipynb

原文链接:https://blog.csdn.net/qq_41033011/article/details/109174046