具有协变量的高斯图回归模型的凸估计
Convex Estimation of Gaussian Graphical Regression Models with Covariates
AI总结：
本文提出了一种凸框架，用于同时估计协变量调整后的均值和精度矩阵，通过多元高斯似然的自然参数化，改进了高维情况下理论保证。
摘要：
高斯图模型（GGMs）被广泛用于恢复随机变量之间的条件独立结构。最近的研究试图将辅助协变量纳入其中以提高估计精度，特别是在共表达数量性状位点（eQTL）研究中，基因表达水平及其条件依赖结构可能受遗传变异影响。现有方法在调整协变量的GGMs中要么限制协变量效应到均值结构，要么在联合估计均值和精度矩阵时导致非凸形式。本文提出了一种凸框架，通过多元高斯似然的自然参数化同时估计协变量调整后的均值和精度矩阵。所得形式允许联合凸优化，并在高维缩放下提供改进的理论保证，其中稀疏性和协变量的维度随样本量增长。我们通过数值模拟支持理论发现，并通过胶质瘤多形体eQTL研究的重新分析和饮食对人类肠道微生物群分析，展示了所提方法的实用价值。
英文摘要：
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such as co-expression quantitative trait locus (eQTL) studies, where both gene expression levels and their conditional dependence structure may be influenced by genetic variants. Existing approaches to covariate-adjusted GGMs either restrict covariate effects to the mean structure or lead to nonconvex formulations when jointly estimating the mean and precision matrix. In this paper, we propose a convex framework that simultaneously estimates the covariate-adjusted mean and precision matrix via a natural parametrization of the multivariate Gaussian likelihood. The 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 and an analysis of diet on the human gut microbiome.
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