Generative Flow Networks: Theory and Applications to Structure Learning

2025-01-09

AI Summary

This work addresses model uncertainty in causal structure learning by enabling reliable posterior inference over both directed acyclic graph (DAG) structures and their associated causal mechanism parameters from observational and interventional data. To this end, we introduce generative flow networks (GFlowNets) to causal discovery for the first time, modeling the target posterior distribution over the discrete DAG space as a learnable, decision-based flow network that permits efficient, unnormalized sampling and inference. Our method integrates variational inference, reinforcement learning, and flow matching principles, achieving end-to-end optimization via forward–backward flow balance constraints, progressive subgraph construction, and a differentiable graph generation architecture. On standard benchmarks, our approach significantly improves posterior diversity and structural accuracy, outperforming conventional score-based search and MCMC methods.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Causal Inference
• Data-driven Learning
• Safe Decision-making

Innovation

• GFlowNets
• Causal Inference
• Bayesian Perspective