请给一个正确的多维Quantile regression C++实现代码及案例

以下是一个基于Eigen和boost库实现的多维Quantile regression C++代码示例：

#include <iostream>
#include <vector>
#include <Eigen/Dense>
#include <boost/math/distributions/normal.hpp>

using namespace Eigen;

// 多维Quantile regression函数
VectorXd quantile_regression(MatrixXd X, VectorXd y, double tau) {
    int n = X.rows(), p = X.cols();
    VectorXd beta(p);
    beta.setZero();
    double epsilon = 1e-6;
    double alpha = 0.05;
    double z = boost::math::quantile(boost::math::normal_distribution<>(0.0, 1.0), 1 - alpha / 2);
    while (true) {
        VectorXd y_star = X * beta;
        VectorXd e = y - y_star;
        VectorXd q(n);
        for (int i = 0; i < n; i++) {
            if (e(i) >= 0) {
                q(i) = tau * e(i);
            } else {
                q(i) = (tau - 1) * e(i);
            }
        }
        MatrixXd W(n, n);
        for (int i = 0; i < n; i++) {
            W(i, i) = tau * (1 - tau);
        }
        MatrixXd XtX = X.transpose() * W * X;
        VectorXd Xty = X.transpose() * W * y;
        JacobiSVD<MatrixXd> svd(XtX, ComputeThinU | ComputeThinV);
        beta = svd.solve(Xty);
        double max_diff = (X * beta - y_star).cwiseAbs().maxCoeff();
        if (max_diff < epsilon) {
            break;
        }
    }
    return beta;
}

int main() {
    std::vector<std::vector<double>> x_data = {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {7, 8}, {8, 9}, {9, 10}};
    std::vector<double> y_data = {2, 3, 4, 5, 6, 7, 8, 9, 10};
    int n = y_data.size(), p = x_data[0].size();
    MatrixXd X(n, p);
    VectorXd y(n);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < p; j++) {
            X(i, j) = x_data[i][j];
        }
        y(i) = y_data[i];
    }
    double tau = 0.5;
    VectorXd beta = quantile_regression(X, y, tau);
    std::cout << "beta = \n" << beta << std::endl;
    return 0;
}

这是一个简单的二维Quantile regression的例子，输入数据为X和y，其中X为n行p列的矩阵，每行代表一个样本的p个特征，y为n维向量，代表每个样本的标签。quantile_regression函数输出一个p维向量beta，代表模型的参数。