Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGs
This work addresses the challenge of causal structure learning for researchers in statistics and machine learning, representing an incremental improvement through enhanced mixing and computational efficiency.
The paper tackles the problem of inferring Bayesian network structures by developing a non-reversible continuous-time Markov chain, the Causal Zig-Zag sampler, which targets probability distributions over Markov equivalence classes of DAGs. The result includes an efficient implementation with new algorithms that significantly improve run-time over the state-of-the-art, as shown empirically.
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.