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正性约束下的贝叶斯图模型：一种可扩展的广义似然方法AI 解读

We develop a computationally scalable Bayesian framework for precision matrix estimation in Gaussian graphical models under total positivity constraints. To overcome the high computational cost of the Gaussian likelihood, we adopt a generalized Bayesian approach based on the $D$-trace loss, which eliminates the log-determinant term and enables efficient optimization while allowing relaxation of positive definiteness during sampling. Sparsity is induced via spike-and-slab…

高维高斯随机矩阵条件数与奇异值的矩界：应用与局限AI 解读

Spectral properties of Gram matrices are central to high dimensional asymptotic analyses of statistical estimators in regression and covariance estimation. These properties, in turn, depend critically on the extreme singular values and condition numbers of Gaussian random matrices. For many applications, sharp positive and negative moment bounds for these quantities are required to control expected prediction risk and related performance metrics. Although extensive work…

协方差与精度矩阵的高维 Bernstein-Von Mises 定理AI 解读

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis focuses on establishing asymptotic normality of the posterior distribution of the entire covariance/precision matrices under specific growth restrictions on $p_n$ and other mild assumptions. In particular, the limiting distribution turns out to…