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 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之间的条件依赖关系提供了强大的框架。揭示条件依赖网络的过程称为结构学习。贝叶斯方法能够衡量条件关系的不确定性并纳入先验信息。然而，由于贝叶斯方法的计算负担，频率学派方法通常更受青睐。过去十年间，贝叶斯方法取得了显著进展，部分方法如今能在数分钟内生成多达千个变量的精确图估计。尽管取得了这些进步，目前仍缺乏对所有近期方法的全面综述或实证比较。本文深入探讨了用于结构学习的广泛贝叶斯方法，并通过模拟研究评估其有效性。我们还展示了如何将贝叶斯结构学习应用于实际数据集，并指明了未来研究方向。本研究为新手、实践者和专家提供了这一动态领域的全面概述。