  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.

Machine Learning;Machine Learning