Differentiable Bayesian Structure Learning with Acyclicity Assurance

TL;DR

This paper introduces a novel differentiable method for Bayesian structure learning that guarantees acyclicity by integrating topological orderings, improving inference efficiency and outperforming existing score-based approaches.

Contribution

It presents a new approach that strictly enforces acyclicity in Bayesian structure learning by combining continuous relaxation with topological orderings.

Findings

Outperforms existing Bayesian score-based methods on simulated data

Reduces inference complexity while ensuring acyclic graph structures

Effective on both simulated and real-world datasets

Abstract

Score-based approaches in the structure learning task are thriving because of their scalability. Continuous relaxation has been the key reason for this advancement. Despite achieving promising outcomes, most of these methods are still struggling to ensure that the graphs generated from the latent space are acyclic by minimizing a defined score. There has also been another trend of permutation-based approaches, which concern the search for the topological ordering of the variables in the directed acyclic graph in order to limit the search space of the graph. In this study, we propose an alternative approach for strictly constraining the acyclicty of the graphs with an integration of the knowledge from the topological orderings. Our approach can reduce inference complexity while ensuring the structures of the generated graphs to be acyclic. Our empirical experiments with simulated and real-world data show that our approach can outperform related Bayesian score-based approaches.