Differentiable Constraint-Based Causal Discovery

Jincheng Zhou, Mengbo Wang, Anqi He, Yumeng Zhou, Hessam Olya, Murat Kocaoglu, Bruno Ribeiro

Keywords: Causal Discovery, Constraint-based, d-Separation, Continuous optimization, Structure learning

TL;DR: We propose a percolation-based differentiable d-separation framework that bridges constraint-based causal discovery methods with differentiable DAG structure learning.

Abstract: Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable $d$-separation scores, obtained through a percolation theory using soft logic. This enables the implementation of a new type of causal discovery method: gradient-based optimization of conditional independence constraints. Empirical evaluations demonstrate the robust performance of our approach in low-sample regimes, surpassing traditional constraint-based and score-based baselines on a real-world dataset. Code implementing the proposed method is publicly available at [https://github.com/PurdueMINDS/DAGPA](https://github.com/PurdueMINDS/DAGPA).

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 25612