An Expectation Conditional Maximization Approach for Gaussian Graphical Models

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally infeasible. We propose a deterministic alternative to estimate Gaussian and Gaussian copula graphical models using an expectation conditional maximization (ECM) algorithm, extending the EM approach from Bayesian variable selection to graphical model estimation. We show that the ECM approach enables fast posterior exploration under a sequence of mixture priors, and can incorporate multiple sources of information. Supplementary materials for this article are available online.

贝叶斯图模型（Bayesian graphical models）是探究多变量间依赖关系的有效工具，尤其适用于存在外部先验信息的场景。在高维情形下，可能的图结构空间会变得极其庞大，即便当前最先进的贝叶斯随机搜索方法也会因计算量过大而难以实施。本文提出一种确定性替代方案，采用期望条件最大化（Expectation Conditional Maximization, ECM）算法对高斯及高斯copula图模型进行估计，将EM方法从贝叶斯变量选择拓展至图模型估计领域。研究表明，该ECM方法可在一系列混合先验下实现快速后验探索，并能够融合多源信息。本文的补充材料可在线获取。