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

Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGs