A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables

2026-05-11

AI Summary

This work addresses the computational challenges of high-dimensional causal structure learning in the presence of latent variables, where reliance on conditional independence tests becomes prohibitively expensive and existing divide-and-conquer methods often assume causal sufficiency, limiting their applicability. To overcome these limitations, the authors propose DiCoLa, a recursive decomposition framework that extends divide-and-conquer strategies to non-causally-sufficient settings for the first time. DiCoLa recursively partitions the global problem into subproblems, enabling efficient inference even when latent variables are present, and incorporates a principled reconstruction step to recover the complete causal graph. Theoretical analysis establishes the completeness and correctness of the approach under latent variable conditions. Empirical results demonstrate that DiCoLa substantially improves the computational efficiency of various causal discovery algorithms and validates its effectiveness on real-world data.

Abstract

Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.

Problem

• causal structure learning
• latent variables
• constraint-based causal discovery
• computational efficiency
• conditional independence

Innovation

• causal discovery
• latent variables
• divide-and-conquer
• recursive decomposition
• conditional independence