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

TL;DR

This paper introduces the Causal Zig-Zag sampler, a non-reversible Markov chain method for sampling over Markov equivalence classes of DAGs, improving mixing and efficiency in Bayesian network structure learning.

Contribution

It proposes a novel non-reversible continuous-time Markov chain with momentum for sampling Markov equivalence classes of DAGs, enhancing mixing and computational efficiency.

Findings

Empirically shows improved mixing with momentum.

Develops algorithms for GES operator moves, improving runtime.

Efficiently samples from posterior distributions over DAGs.

Abstract

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 run-time.