Bayesian Structure Learning with Generative Flow Networks
This addresses the challenge of Bayesian structure learning for researchers in probabilistic graphical models, offering a novel method but is incremental as it applies an existing framework (GFlowNets) to a specific domain.
The authors tackled the problem of inferring a distribution over directed acyclic graph (DAG) structures in Bayesian networks from data, proposing DAG-GFlowNet as an alternative to MCMC methods, and showed it provides an accurate posterior approximation and compares favorably against other methods.
In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) structure of Bayesian networks, from data. Defining such a distribution is very challenging, due to the combinatorially large sample space, and approximations based on MCMC are often required. Recently, a novel class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling of discrete and composite objects, such as graphs. In this work, we propose to use a GFlowNet as an alternative to MCMC for approximating the posterior distribution over the structure of Bayesian networks, given a dataset of observations. Generating a sample DAG from this approximate distribution is viewed as a sequential decision problem, where the graph is constructed one edge at a time, based on learned transition probabilities. Through evaluation on both simulated and real data, we show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs, and it compares favorably against other methods based on MCMC or variational inference.