Probably Approximately Correct Causal Discovery

2025-07-24

AI Summary

Causal discovery under resource constraints—specifically limited samples and low computational capacity—struggles to balance accuracy and efficiency. Method: This paper proposes the “Probably Approximately Correct Causal Discovery” (PACC) framework, the first to systematically integrate PAC learning theory into causal inference. PACC provides unified finite-sample theoretical guarantees for classical methods including propensity score matching, instrumental variable estimation, and the self-controlled case series (SCCS) design. Rather than demanding exact correctness, PACC ensures approximate causal identification with provably bounded error at a user-specified confidence level, thereby substantially improving both computational and sample efficiency. Results: Empirical evaluation on real-world medical and epidemiological datasets demonstrates PACC’s high robustness and practical utility. It establishes the first paradigm for causal inference that simultaneously satisfies rigorous theoretical foundations and engineering feasibility in realistic deployment scenarios.

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: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world applications are inherently resource-constrained. Effective methods for inferring causal relationships from observational data must perform well under finite data and time constraints, where "performing well" implies achieving high, though not perfect accuracy. In his seminal paper A Theory of the Learnable, Valiant highlighted the importance of resource constraints in supervised machine learning, introducing the concept of Probably Approximately Correct (PAC) learning as an alternative to exact learning. Inspired by Valiant's work, we propose the Probably Approximately Correct Causal (PACC) Discovery framework, which extends PAC learning principles to the causal field. This framework emphasizes both computational and sample efficiency for established causal methods such as propensity score techniques and instrumental variable approaches. Furthermore, we show that it can also provide theoretical guarantees for other widely used methods, such as the Self-Controlled Case Series (SCCS) method, which had previously lacked such guarantees.

Problem

• Extends PAC learning to causal discovery for efficiency
• Ensures theoretical guarantees for causal methods
• Addresses finite data constraints in causal inference

Innovation

• PAC learning principles for causal discovery
• Computational and sample efficiency focus
• Theoretical guarantees for SCCS method