Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian methods can measure the uncertainty of conditional relationships and include prior information. However, frequentist methods are often preferred due to the computational burden of the Bayesian approach. Over the last decade, Bayesian methods have seen substantial improvements, with some now capable of generating accurate estimates of graphs up to a thousand variables in mere minutes. Despite these advancements, a comprehensive review or empirical comparison of all recent methods has not been conducted. This paper delves into a wide spectrum of Bayesian approaches used for structure learning and evaluates their efficacy through a comprehensive simulation study. We also demonstrate how to apply Bayesian structure learning to a real-world data set and provide directions for future research. This study gives an exhaustive overview of this dynamic field for newcomers, practitioners, and experts.

翻译：高斯图模型为揭示多元变量间的条件依赖结构提供了强大框架。揭示条件依赖网络的过程被称为结构学习。贝叶斯方法能够量化条件关系的不确定性并纳入先验信息。然而，由于贝叶斯方法存在计算负担，频率主义方法常更受青睐。过去十年间，贝叶斯方法已取得显著改进，部分方法现能在数分钟内对上千变量生成精确的图估计。尽管存在这些进展，目前尚未对近期所有方法进行系统性综述或实证比较。本文深入探讨了用于结构学习的各类贝叶斯方法，并通过综合模拟研究评估其效能。我们同时展示了如何将贝叶斯结构学习应用于实际数据集，并为未来研究方向提供指引。本研究为该动态领域的新学者、实践者和专家提供了全面综述。