Structure Learning with Adaptive Random Neighborhood Informed MCMC
This work addresses the challenge of sampling from posterior distributions on DAGs in high-dimensional settings, which is incremental but offers practical improvements for Bayesian causal inference.
The paper tackles the problem of structure learning for Directed Acyclic Graphs (DAGs) from observational data by introducing PARNI-DAG, a novel MCMC sampler that achieves better mixing properties and scalability, as demonstrated empirically through improved efficiency and accuracy in learning DAG structures.
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.