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

arXiv: https://arxiv.org/abs/2310.05655 · HTML: https://mlsanity.com/paper/2310.05655/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 11 of 11)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [A Transformational Characterization of Equivalent Bayesian Network Structures](https://mlsanity.com/paper/1302.4938/) (2013)
- [Partition MCMC for inference on acyclic digraphs](https://mlsanity.com/paper/1504.05006/) (2015)
- [Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo](https://mlsanity.com/paper/1611.07873/) (2016)
- [Being Bayesian about Network Structure](https://mlsanity.com/paper/1301.3856/) (2013)
- [Minimal I-MAP MCMC for Scalable Structure Discovery in Causal DAG Models](https://mlsanity.com/paper/1803.05554/) (2018)

## Built on by (most cited first, 2 of 2)

- [Greedy equivalence search for nonparametric graphical models](https://mlsanity.com/paper/2406.17228/) (2024)
- [A fast non-reversible sampler for Bayesian mixture models](https://mlsanity.com/paper/2510.03226/) (2025)

## Abstract (arXiv)

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.