Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is straightforward in this setup, inferring the underlying graph is a challenge driven by the computational difficulty in exploring the space of decomposable graphs. This work makes two contributions to address this problem. First, we provide sufficient and necessary conditions for when multi-edge perturbations maintain decomposability of the graph. Using these, we characterize a simple class of partitions that efficiently classify all edge perturbations by whether they maintain decomposability. Second, we propose a novel parallel non-reversible Markov chain Monte Carlo sampler for distributions over junction tree representations of the graph. At every step, the parallel sampler executes simultaneously all edge perturbations within a partition. Through simulations, we demonstrate the efficiency of our new edge perturbation conditions and class of partitions. We find that our parallel sampler yields improved mixing properties in comparison to the single-move variate, and outperforms current state-of-the-arts methods in terms of accuracy and computational efficiency. The implementation of our work is available in the Python package parallelDG.

翻译：无向图模型的贝叶斯推断主要局限于可分解图类，因其具备丰富的性质使其适用于高维问题。尽管在此框架下参数推断较为直接，但底层图结构的推断仍面临挑战，其根本原因在于探索可分解图空间的计算困难。本文针对该问题提出两项贡献：首先，我们给出多边扰动维持图可分解性的充分必要条件。基于此，我们刻画了一类简单划分方法，能高效区分所有边扰动是否保持可分解性。其次，我们提出一种新型并行非可逆马尔可夫链蒙特卡洛采样器，用于图结构联结树表示的分布采样。每步迭代中，该并行采样器同步执行某个划分内的所有边扰动。通过仿真实验，我们验证了新提出的边扰动条件及划分方法的效率。结果表明，相较于单步移动变体，我们的并行采样器具有更优的混合性质，并在精度与计算效率上均超越当前最优方法。本研究的实现代码已开源至Python软件包parallelDG。