Bayesian methods for learning Gaussian graphical models offer a robust framework that addresses model uncertainty and incorporates prior knowledge. Despite their theoretical strengths, the applicability of Bayesian methods is often constrained by computational needs, especially in modern contexts involving thousands of variables. To overcome this issue, we introduce two novel Markov chain Monte Carlo (MCMC) search algorithms that have a significantly lower computational cost than leading Bayesian approaches. Our proposed MCMC-based search algorithms use the marginal pseudo-likelihood approach to bypass the complexities of computing intractable normalizing constants and iterative precision matrix sampling. These algorithms can deliver reliable results in mere minutes on standard computers, even for large-scale problems with one thousand variables. Furthermore, our proposed method is capable of addressing model uncertainty by efficiently exploring the full posterior graph space. Our simulation study indicates that the proposed algorithms, particularly for large-scale sparse graphs, outperform the leading Bayesian approaches in terms of computational efficiency and precision. The implementation supporting the new approach is available through the R package BDgraph.

翻译：贝叶斯方法用于学习高斯图模型提供了一个稳健的框架，能够处理模型不确定性并融入先验知识。尽管具有理论优势，贝叶斯方法的适用性常受计算需求限制，尤其在涉及数千个变量的现代场景中。为解决这一问题，我们引入了两种新颖的马尔可夫链蒙特卡洛（MCMC）搜索算法，其计算成本显著低于主流贝叶斯方法。我们提出的基于MCMC的搜索算法利用边际伪似然方法，避免了计算复杂的归一化常数和迭代精度矩阵采样的难题。这些算法即使在处理包含一千个变量的大规模问题时，也能在标准计算机上仅需数分钟即可获得可靠结果。此外，我们的方法能够通过有效探索全后验图空间来应对模型不确定性。仿真研究表明，所提算法在处理大规模稀疏图时，在计算效率和精度上均优于主流贝叶斯方法。支持新方法的实现可通过R包BDgraph获取。