带协变量的高斯图回归模型的凸估计
统计方法学
2026-03-31 v2 机器学习
摘要
高斯图模型（GGMs）广泛用于恢复随机变量之间的条件独立结构。近期研究试图纳入辅助协变量以改进估计，尤其是在共表达定量性位点（eQTL）研究中，后者涉及基因表达水平及其条件依赖结构可能受基因变异影响。在本文中，我们提出了一个凸框架，通过对多元高斯似然函数进行自然参数化，同时估计协变量调整后的均值和精度矩阵。 resulting formulation enables joint convex optimization and yields improved theoretical guarantees under high-dimensional scaling, where the sparsity and dimension of covariates grow with the sample size. We support our theoretical findings with numerical simulations and demonstrate the practical utility of the proposed method through a reanalysis of an eQTL study of glioblastoma multiforme (GBM), an aggressive form of brain cancer.
引用
@article{arxiv.2410.06326,
title = {Convex estimation of Gaussian graphical regression models with covariates},
author = {Ruobin Liu and Guo Yu},
journal= {arXiv preprint arXiv:2410.06326},
year = {2026}
}