Generative Flow Networks: Theory and Applications to Structure Learning

TL;DR

This paper introduces Generative Flow Networks (GFlowNets), a new probabilistic modeling approach for structure learning in causal Bayesian networks, enabling approximation of the posterior distribution over DAGs from data.

Contribution

It presents GFlowNets as a novel class of models for sampling complex discrete structures, with theoretical foundations and applications to causal structure learning.

Findings

GFlowNets effectively approximate the posterior over DAG structures.

The approach integrates with Bayesian causal inference.

Extensions beyond discrete problems demonstrated.

Abstract

Without any assumptions about data generation, multiple causal models may explain our observations equally well. To avoid selecting a single arbitrary model that could result in unsafe decisions if it does not match reality, it is therefore essential to maintain a notion of epistemic uncertainty about our possible candidates. This thesis studies the problem of structure learning from a Bayesian perspective, approximating the posterior distribution over the structure of a causal model, represented as a directed acyclic graph (DAG), given data. It introduces Generative Flow Networks (GFlowNets), a novel class of probabilistic models designed for modeling distributions over discrete and compositional objects such as graphs. They treat generation as a sequential decision making problem, constructing samples of a target distribution defined up to a normalization constant piece by piece. In the first part of this thesis, we present the mathematical foundations of GFlowNets, their connections to existing domains of machine learning and statistics such as variational inference and reinforcement learning, and their extensions beyond discrete problems. In the second part of this thesis, we show how GFlowNets can approximate the posterior distribution over DAG structures of causal Bayesian Networks, along with the parameters of its causal mechanisms, given observational and experimental data.