Learning Equivalence Classes of Bayesian Network Structures with GFlowNet

Michelle Liu, Zhaocheng Zhu, Olexa Bilaniuk, Emmanuel Bengio

Authors that are also TMLR Expert Reviewers: ~Emmanuel_Bengio1

Abstract: Understanding the causal graph underlying a system is essential for enabling causal inference, particularly in fields such as medicine and genetics. Identifying a causal Directed Acyclic Graph (DAG) from observational data alone is challenging because multiple DAGs can encode the same set of conditional independencies. These equivalent DAGs form a Markov Equivalence Class (MEC), which is represented by a Completed Partially Directed Acyclic Graph (CPDAG). Effectively approximating the CPDAG is crucial because it facilitates narrowing down the set of possible causal graphs underlying the data. We introduce CPDAG-GFN, a novel approach that uses a Generative Flow Network (GFlowNet) to learn a posterior distribution over CPDAGs. From this distribution, we sample high-reward CPDAG candidates that approximate the ground truth, with rewards determined by a score function that quantifies how well each graph fits the data. Additionally, CPDAG-GFN incorporates a sparsity-preferring filter to enhance the set of CPDAG candidates and improve their alignment with the ground truth. Experimental results on both simulated and real-world datasets demonstrate that CPDAG-GFN performs competitively with established methods for learning CPDAG candidates from observational data.

Certifications: Expert Certification

Submission Length: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=7gqzvKJoTb

Changes Since Last Submission:

* Refined the introduction to better highlight the goal of our work.
* Edited the method section
* Included TPR/FPR results in Appendix I.
* Added NOTEARS as a baseline in Appendix H.
* Edited the Experimental Evaluation section to improve clarity and provide more details.

Assigned Action Editor: ~Jean_Honorio1

Submission Number: 4372