写成其python代码

以下是将ObjFun写成其局部近似函数ApproxFun的Python代码：

import numpy as np

def ObjFun(x, y, beta):
    """
    Logistic regression loss function
    :param beta: model parameter vector
    :param x: feature matrix
    :param y: label vector
    :return: loss value
    """
    n = x.shape[0]
    p = x.shape[1]
    sigmoid = 1 / (1 + np.exp(-np.dot(x, beta)))
    pred = np.clip(sigmoid, 1e-15, 1 - 1e-15)
    ObjVal = -np.sum(y * np.log(pred) + (1 - y) * np.log(1 - pred)) / n
    return ObjVal

def ApproxFun(XStar, x, ObjVal, GradVect, HessMat):
    """
    The Approximation function value at local optimizer XStar
    :param XStar: The local optimizer
    :param x: feature matrix
    :param ObjVal: The original objective function value at CurrX
    :param GradVect: The gradient vector of original objective function at CurrX
    :param HessMat: The Hessian matrix of original objective function at CurrX
    :return: The approximation function value at XStar
    """
    DiffX = np.array(XStar - x) 
    ApproxVal = 0.5 * DiffX.T @ HessMat @ DiffX + GradVect.T @ DiffX + ObjVal
    return ApproxVal

其中，ObjFun是逻辑回归的损失函数，用于计算当前beta对应的模型在训练集上的损失值；ApproxFun是ObjFun的局部近似函数，用于某些优化算法中计算当前局部最优点的近似值。