Differentiable Constraint-Based Causal Discovery

2025-10-24

AI Summary

Causal discovery aims to infer causal structures among variables from observational data, forming the foundation for AI-driven decision-making and intervention. Existing constraint-based methods (e.g., PC) rely on conditional independence tests but suffer from poor statistical power in small-sample regimes; score-based approaches (e.g., NOTEARS) enable differentiable optimization yet neglect explicit independence constraints. This paper proposes the first differentiable d-separation scoring framework integrating soft logic and percolation theory: conditional independencies are encoded as soft logical formulas; a continuous, differentiable d-separation metric is constructed via percolation-theoretic principles; and the resulting objective is embedded into a gradient-based end-to-end learning framework for causal graph estimation. Our method unifies the statistical rigor of constraint-based methods with the optimization flexibility of score-based ones. It achieves significant improvements over state-of-the-art baselines under limited samples and establishes new SOTA performance across multiple real-world benchmarks. Code and data are publicly available.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

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: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Developing differentiable d-separation scores for causal discovery
• Enabling gradient-based optimization of conditional independence constraints
• Improving robust performance in low-sample regimes over traditional methods

Innovation

• Differentiable d-separation scores via soft logic
• Gradient-based optimization of independence constraints
• Robust causal discovery in low-sample regimes