DiBS: Differentiable Bayesian Structure Learning

TL;DR

DiBS introduces a fully differentiable framework for Bayesian structure learning that enables joint inference of graph structures and parameters, applicable to complex models including neural networks, and outperforms existing methods.

Contribution

A novel differentiable approach for Bayesian structure learning that is agnostic to local distribution forms and supports joint inference of structure and parameters.

Findings

Outperforms related methods on simulated data

Effective in real-world Bayesian network inference

Supports complex models with neural network dependencies

Abstract

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our formulation directly applicable to posterior inference of complex Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. Using DiBS, we devise an efficient, general purpose variational inference method for approximating distributions over structural models. In evaluations on simulated and real-world data, our method significantly outperforms related approaches to joint posterior inference.