In the context of inferring a Bayesian network structure (directed acyclic graph, DAG for short), we devise a non-reversible continuous time Markov chain, the "Causal Zig-Zag sampler", that targets a probability distribution over classes of observationally equivalent (Markov equivalent) DAGs. The classes are represented as completed partially directed acyclic graphs (CPDAGs). The non-reversible Markov chain relies on the operators used in Chickering's Greedy Equivalence Search (GES) and is endowed with a momentum variable, which improves mixing significantly as we show empirically. The possible target distributions include posterior distributions based on a prior over DAGs and a Markov equivalent likelihood. We offer an efficient implementation wherein we develop new algorithms for listing, counting, uniformly sampling, and applying possible moves of the GES operators, all of which significantly improve upon the state-of-the-art.

翻译：在推断贝叶斯网络结构（即有向无环图，简称DAG）的背景下，我们设计了一种不可逆连续时间马尔可夫链——“因果锯齿采样器”——用于对观测等价（马尔可夫等价）DAG类上的概率分布进行采样。这些等价类以完全部分有向无环图（CPDAG）的形式表示。该不可逆马尔可夫链基于Chickering的贪婪等价搜索（GES）算子，并引入了动量变量，经验表明这显著改善了混合性能。可能的采样目标分布包括基于DAG先验分布和马尔可夫等价似然的后验分布。我们提供了一种高效实现方式，其中开发了新算法用于列举、计数、均匀采样以及应用GES算子的可能操作，这些算法均显著优于现有最优方法。