Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models

2024-05-23

AI Summary

Global causal discovery from high-dimensional nonlinear observational data faces challenges in uniquely identifying the underlying DAG, while existing methods are hindered by the curse of dimensionality or restrictive parametric assumptions—such as linearity or additive noise. Method: This paper proposes a topological-sorting-driven hierarchical causal ordering framework. It is the first to encode ancestral relationships as a compact causal order and integrates local conditional set search with nonparametric conditional independence testing, thereby relaxing linearity and additive-noise constraints. Contribution/Results: We provide theoretical guarantees for correctness and polynomial-time complexity. Empirical evaluation on synthetic data demonstrates significantly higher edge identification accuracy than state-of-the-art methods, while maintaining compatibility with both linear and arbitrary nonlinear additive-noise models.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Learning the unique directed acyclic graph corresponding to an unknown causal model is a challenging task. Methods based on functional causal models can identify a unique graph, but either suffer from the curse of dimensionality or impose strong parametric assumptions. To address these challenges, we propose a novel hybrid approach for global causal discovery in observational data that leverages local causal substructures. We first present a topological sorting algorithm that leverages ancestral relationships in linear structural causal models to establish a compact top-down hierarchical ordering, encoding more causal information than linear orderings produced by existing methods. We demonstrate that this approach generalizes to nonlinear settings with arbitrary noise. We then introduce a nonparametric constraint-based algorithm that prunes spurious edges by searching for local conditioning sets, achieving greater accuracy than current methods. We provide theoretical guarantees for correctness and worst-case polynomial time complexities, with empirical validation on synthetic data.

Problem

• Causal Inference
• Complex Data
• Non-strict Assumptions

Innovation

• Causal Inference
• Hybrid Top-Down Strategy
• Local Search Optimization