使用python实现逻辑回归函数

Sure, no problem! Here is an implementation of the logistic regression function in Python:

import numpy as np

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

class LogisticRegression:
    def __init__(self, lr=0.01, num_iter=100000, fit_intercept=True, verbose=False):
        self.lr = lr
        self.num_iter = num_iter
        self.fit_intercept = fit_intercept
        self.verbose = verbose
    
    def add_intercept(self, X):
        intercept = np.ones((X.shape[0], 1))
        return np.concatenate((intercept, X), axis=1)

    def fit(self, X, y):
        if self.fit_intercept:
            X = self.add_intercept(X)

        # initialize weights
        self.theta = np.zeros(X.shape[1])

        # gradient descent
        for i in range(self.num_iter):
            z = np.dot(X, self.theta)
            h = sigmoid(z)
            gradient = np.dot(X.T, (h - y)) / y.size
            self.theta -= self.lr * gradient
            
            if self.verbose and i % 10000 == 0:
                z = np.dot(X, self.theta)
                h = sigmoid(z)
                print(f'loss: {self._loss(h, y)} \t')

    def predict_prob(self, X):
        if self.fit_intercept:
            X = self.add_intercept(X)

        return sigmoid(np.dot(X, self.theta))

    def predict(self, X, threshold=0.5):
        return self.predict_prob(X) >= threshold

    def _loss(self, h, y):
        return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()

This implementation includes a `sigmoid` function, which is used to calculate the probability of the target variable being 1, given the input features. The `LogisticRegression` class fits the logistic regression model using gradient descent, and includes methods for predicting probabilities and binary classifications. If `fit_intercept` is set to `True`, the model will also fit an intercept term to the data.