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.

翻译：基于约束的因果发现被广泛用于学习因果结构，但因其高度依赖条件独立性检验，在高维场景下计算成本高昂。为缓解此局限，已有许多分而治之框架被提出，但多数假设因果充分性（即不存在隐变量）。在本文中，我们证明分而治之策略可在理论上超越因果充分性假设，推广至存在隐变量的场景。具体而言，我们提出一个名为DiCoLa的递归分解框架，使得在隐变量存在时仍可实现分而治之的因果发现。该框架通过递归方式将全局学习任务分解为更小的子问题，并通过基于原理的重构步骤整合其解，以恢复全局结构。我们从理论上建立了所提框架的正确性与完备性。在合成数据上的大量实验表明，我们的方法能显著提升多种因果发现算法的计算效率；而在真实世界数据集上的实验进一步验证了其实际有效性。