Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network

TL;DR

This paper introduces JSP-GFN, a novel method using a single Generative Flow Network to jointly infer the structure and parameters of Bayesian Networks, accommodating complex models including neural networks.

Contribution

It extends GFlowNets to approximate the joint posterior over both structure and parameters of Bayesian Networks in a unified framework.

Findings

Accurately approximates the joint posterior of structure and parameters.

Performs favorably against existing methods on simulated and real data.

Applicable to non-linear models with neural network parametrizations.

Abstract

Generative Flow Networks (GFlowNets), a class of generative models over discrete and structured sample spaces, have been previously applied to the problem of inferring the marginal posterior distribution over the directed acyclic graph (DAG) of a Bayesian Network, given a dataset of observations. Based on recent advances extending this framework to non-discrete sample spaces, we propose in this paper to approximate the joint posterior over not only the structure of a Bayesian Network, but also the parameters of its conditional probability distributions. We use a single GFlowNet whose sampling policy follows a two-phase process: the DAG is first generated sequentially one edge at a time, and then the corresponding parameters are picked once the full structure is known. Since the parameters are included in the posterior distribution, this leaves more flexibility for the local probability models of the Bayesian Network, making our approach applicable even to non-linear models parametrized by neural networks. We show that our method, called JSP-GFN, offers an accurate approximation of the joint posterior, while comparing favorably against existing methods on both simulated and real data.