admm-lasso加权分位数回归代码

以下是admm-lasso加权分位数回归的代码示例：

import numpy as np
from scipy.linalg import norm

def admm_lasso_wqr(X, y, w, lam, rho, alpha, max_iter=1000, tol=1e-4):
    n_samples, n_features = X.shape
    z = np.zeros(n_features)
    u = np.zeros(n_features)
    q = np.zeros(n_samples)
    p = np.percentile(np.abs(y - np.mean(y)), alpha)
    
    Xw = X * np.sqrt(w.reshape(-1, 1))
    yw = y * np.sqrt(w)
    
    inv = np.linalg.inv(Xw.T @ Xw + rho * np.identity(n_features))
    
    for i in range(max_iter):
        z_old = z.copy()
        q_old = q.copy()
        
        # update z
        z = inv @ (Xw.T @ yw + rho * (u - z))
        
        # update q
        q = np.maximum(y - X @ z - p, 0) - np.maximum(-y + X @ z - p, 0)
        
        # update u
        u = u + rho * (z - q)
        
        # check convergence
        r_norm = norm(z - q)
        s_norm = norm(-rho * (z - z_old))
        eps_pri = np.sqrt(n_features) * tol + tol * max(norm(X @ z), norm(-q))
        eps_dual = np.sqrt(n_features) * tol + tol * norm(rho * u)
        if r_norm < eps_pri and s_norm < eps_dual:
            break
            
    beta = z.copy()
    return beta

其中，`X`是输入特征矩阵，`y`是目标变量向量，`w`是样本权重向量，`lam`是L1正则化系数，`rho`是ADMM参数，`alpha`是分位数水平，`max_iter`是最大迭代次数，`tol`是收敛阈值。

在函数中，首先根据样本权重`w`对输入特征矩阵和目标变量向量进行加权处理。然后，初始化变量`z`、`u`、`q`，并根据分位数水平`alpha`计算分位数`p`。接着，使用ADMM算法对模型进行迭代优化，更新变量`z`、`q`、`u`，直到满足收敛条件为止。最后，返回稀疏系数向量`beta`。