Structure Learning with Adaptive Random Neighborhood Informed MCMC

TL;DR

This paper presents PARNI-DAG, an innovative MCMC sampler for Bayesian structure learning of DAGs that improves mixing efficiency and scalability through adaptive proposals and pre-tuning, enabling better exploration of high-dimensional graph spaces.

Contribution

The paper introduces PARNI-DAG, a novel adaptive MCMC algorithm with a pre-tuning procedure for efficient Bayesian DAG structure learning under observational data.

Findings

PARNI-DAG converges quickly to high-probability DAG regions.

The sampler exhibits improved mixing properties over existing methods.

It demonstrates high accuracy in structure learning across various experiments.

Abstract

In this paper, we introduce a novel MCMC sampler, PARNI-DAG, for a fully-Bayesian approach to the problem of structure learning under observational data. Under the assumption of causal sufficiency, the algorithm allows for approximate sampling directly from the posterior distribution on Directed Acyclic Graphs (DAGs). PARNI-DAG performs efficient sampling of DAGs via locally informed, adaptive random neighborhood proposal that results in better mixing properties. In addition, to ensure better scalability with the number of nodes, we couple PARNI-DAG with a pre-tuning procedure of the sampler's parameters that exploits a skeleton graph derived through some constraint-based or scoring-based algorithms. Thanks to these novel features, PARNI-DAG quickly converges to high-probability regions and is less likely to get stuck in local modes in the presence of high correlation between nodes in high-dimensional settings. After introducing the technical novelties in PARNI-DAG, we empirically demonstrate its mixing efficiency and accuracy in learning DAG structures on a variety of experiments.