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

• URL: http://arxiv.org/abs/2405.14496v4
• Date: Thu, 07 Nov 2024 22:37:35 GMT
• Title: Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models
• Authors: Sujai Hiremath, Jacqueline R. M. A. Maasch, Mengxiao Gao, Promit Ghosal, Kyra Gan,
• Abstract summary: Methods based on functional causal models can identify a unique graph, but suffer from the curse of dimensionality or impose strong parametric assumptions. We propose a novel hybrid approach for global causal discovery in observational data that leverages local causal substructures. We provide theoretical guarantees for correctness and worst-case time complexities, with empirical validation on synthetic data.
• Score: 2.0738462952016232
• License:
• 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 equation 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.

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