Bayesian Structure Learning with Generative Flow Networks

Abstract

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.

Robust Scheduling with GFlowNets

“…Generative Flow Networks. GFlowNets have been applied to generating small molecules (Bengio et al, 2021a), Bayesian networks (Deleu et al, 2022), discrete images , and biological sequences . We extend its application to scheduling, a classical combinatorial optimization problem.…”

“…Note that this differs from previous work that tests the generalization of GFlowNets to unseen data (Nica et al, 2022). To control the selectiveness of the generator, previous works augment the reward with a fixed temperature (Bengio et al, 2021a;Deleu et al, 2022;. Instead, we condition the policy neural network on the temperature term which allows us to tune the selectiveness of the generator at inference time.…”

GFlowCausal: Generative Flow Networks for Causal Discovery

“…Remark 2 1) We find the process of evaluating graphs is dominating in the total running time. Compared to Deleu et al [2022], our ordering generation approach does not spend much time computing rewards; 2) If we evaluate DAG every state transition, which is the exact graph generation, we need to replace I st+1=s f r(s t+1 , X) with r(s t+1 , X) in (12). However, the search space increases exponentially and it becomes more expensive to compute the loss function with this approach.…”

“…In this section we compare GFlowCausal with DAG-GFlowNet Deleu et al [2022] (a GFlowNetsbased bayesian structure learning method) to show the effectiveness and efficiency of our proposed approach. DAG-GFlowNet focuses on bayesian structure learning, which is similar to our causal discovery task and it also incorporates the idea of adding edges gradually.…”

“…The batch size is 64 and the number of samples is 1000. Following the setting in Deleu et al [2022] we also show the expected SHD of both approaches, which is given by…”