Generative Flow Networks: Theory and Applications to Structure Learning
It addresses the need to maintain epistemic uncertainty in causal inference to avoid unsafe decisions, which is crucial for fields like statistics and machine learning, though it appears incremental in applying GFlowNets to this domain.
The paper tackles the problem of structure learning for causal models by approximating the posterior distribution over directed acyclic graphs (DAGs) using Generative Flow Networks (GFlowNets), a novel probabilistic model for discrete and compositional objects, without specifying concrete numerical results.
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.