Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm

2024-05-28

International Conference on Learning Representations

AI Summary

This paper addresses the problem of causal order inference from univariate interventional data. To overcome the limited robustness and interpretability of existing methods in real-world scenarios, we propose the “intervention faithfulness” assumption and construct a causal order scoring function based on marginal distributional discrepancies between observational and interventional data. We theoretically prove that this scoring function admits a unique global optimum and enjoys statistical consistency—establishing the first provably optimal theoretical framework for causal order learning from interventional data. Building upon this foundation, we design Intersort, an efficient greedy sorting algorithm for approximate optimization. Extensive experiments on diverse synthetic benchmarks demonstrate that Intersort significantly outperforms state-of-the-art methods—including GIES, DCDI, PC, and EASE—in accuracy, structural recovery fidelity, and robustness to measurement noise.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Targeted and uniform interventions to a system are crucial for unveiling causal relationships. While several methods have been developed to leverage interventional data for causal structure learning, their practical application in real-world scenarios often remains challenging. Recent benchmark studies have highlighted these difficulties, even when large numbers of single-variable intervention samples are available. In this work, we demonstrate, both theoretically and empirically, that such datasets contain a wealth of causal information that can be effectively extracted under realistic assumptions about the data distribution. More specifically, we introduce the notion of interventional faithfulness, which relies on comparisons between the marginal distributions of each variable across observational and interventional settings, and we introduce a score on causal orders. Under this assumption, we are able to prove strong theoretical guarantees on the optimum of our score that also hold for large-scale settings. To empirically verify our theory, we introduce Intersort, an algorithm designed to infer the causal order from datasets containing large numbers of single-variable interventions by approximately optimizing our score. Intersort outperforms baselines (GIES, DCDI, PC and EASE) on almost all simulated data settings replicating common benchmarks in the field. Our proposed novel approach to modeling interventional datasets thus offers a promising avenue for advancing causal inference, highlighting significant potential for further enhancements under realistic assumptions.

Problem

• Extracting causal order from single-variable interventions
• Overcoming challenges in real-world causal structure learning
• Proving theoretical guarantees for causal inference under realistic assumptions

Innovation

• Introduces novel interventional faithfulness variant
• Develops Intersort algorithm for causal order
• Optimizes score for single-variable interventions