Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds sample size, penalized methods like lasso have been developed to address sparsity challenges. Bayesian methods, initially connected to quantile regression via the asymmetric Laplace likelihood, have also evolved, though issues with posterior variance have led to new approaches, including pseudo/score likelihoods. This paper presents a novel probabilistic machine learning approach for high-dimensional quantile prediction. It uses a pseudo-Bayesian framework with a scaled Student-t prior and Langevin Monte Carlo for efficient computation. The method demonstrates strong theoretical guarantees, through PAC-Bayes bounds, that establish non-asymptotic oracle inequalities, showing minimax-optimal prediction error and adaptability to unknown sparsity. Its effectiveness is validated through simulations and real-world data, where it performs competitively against established frequentist and Bayesian techniques.

本研究解决了在高维环境中分位数回归面临的挑战，尤其是当协变量数量超过样本量时。提出了一种新颖的伪贝叶斯框架，结合缩放的学生-t先验和Langevin蒙特卡洛方法，有效地进行高维分位数预测。研究表明，该方法在非渐近优化预测误差和适应未知稀疏性方面具有较强的理论保证，并在模拟和实际数据中表现出竞争力。

高维分位数预测的稀疏PAC-贝叶斯方法