Permutation-based Inference for Variational Learning of Directed Acyclic Graphs
Abstract
Estimating the structure of Bayesian networks as directed acyclic graphs (DAGs) from observational data is a fundamental challenge, particularly in causal discovery. Bayesian approaches excel by quantifying uncertainty and addressing identifiability, but key obstacles remain: (i) representing distributions over DAGs and (ii) estimating a posterior in the underlying combinatorial space. We introduce PIVID, a method that jointly infers a distribution over permutations and DAGs using variational inference and continuous relaxations of discrete distributions. Through experiments on synthetic and real-world datasets, we show that PIVID can outperform deterministic and Bayesian approaches, achieving superior accuracy-uncertainty trade-offs while scaling efficiently with the number of variables.
Cite
@article{arxiv.2402.02644,
title = {Permutation-based Inference for Variational Learning of Directed Acyclic Graphs},
author = {Edwin V. Bonilla and Pantelis Elinas and He Zhao and Maurizio Filippone and Vassili Kitsios and Terry O'Kane},
journal= {arXiv preprint arXiv:2402.02644},
year = {2026}
}