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.

在推断贝叶斯网络结构（有向无环图，DAG）的背景下，我们设计了一种非可逆连续时间马尔可夫链，称为 “因果 Zig-Zag 采样器”，该采样器针对一类观测等效（Markov 等价）DAG 的概率分布。这些类别以完成的部分有向无环图（CPDAG）表示。非可逆马尔可夫链依赖于 Chickering 的贪婪等价搜索（GES）中使用的操作符，并以动量变量进行了改进，从实证结果上显示其混合效果显著。可能的目标分布包括基于 DAG 先验和 Markov 等价似然的后验分布。我们提供了一种高效的实现，其中我们开发了新的算法来列出、计数、均匀采样和应用 GES 操作符的可能移动，所有这些都显著改进了现有技术水平。