Differentiable Constraint-Based Causal Discovery

TL;DR

This paper introduces a novel differentiable approach to causal discovery that combines the rigor of constraint-based methods with the flexibility of gradient-based optimization, excelling especially in low-sample scenarios.

Contribution

It develops differentiable d-separation scores using soft logic and percolation theory, enabling gradient-based causal discovery that outperforms traditional methods in small sample settings.

Findings

Outperforms traditional methods in low-sample regimes

Demonstrates robustness on real-world datasets

Provides publicly available code and data

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 and data of the proposed method are publicly available at https://github$.$com/PurdueMINDS/DAGPA.