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

arXiv: https://arxiv.org/abs/2605.10651 · HTML: https://mlsanity.com/paper/2605.10651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 74 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 27 of 27)

- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution](https://mlsanity.com/paper/1801.04016/) (2018)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Causal Structure Discovery between Clusters of Nodes Induced by Latent Factors](https://mlsanity.com/paper/2207.01237/) (2022)
- [Robust causal structure learning with some hidden variables](https://mlsanity.com/paper/1708.01151/) (2017)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [Learning Bayesian Networks in the Presence of Structural Side Information](https://mlsanity.com/paper/2112.10884/) (2021)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables](https://mlsanity.com/paper/2308.06718/) (2023)
- [Local Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2405.16225/) (2024)
- [Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables](https://mlsanity.com/paper/2208.06935/) (2022)
- [From Temporal to Contemporaneous Iterative Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2306.00624/) (2023)
- [SADA: A General Framework to Support Robust Causation Discovery with Theoretical Guarantee](https://mlsanity.com/paper/1707.01283/) (2017)
- [Bayesian Structure Learning by Recursive Bootstrap](https://mlsanity.com/paper/1809.04828/) (2018)
- [Causal Structural Learning Via Local Graphs](https://mlsanity.com/paper/2107.03597/) (2021)
- [MIDAS - An Influence Diagram for Management of Mildew in Winter Wheat](https://mlsanity.com/paper/1302.3587/) (2013)
- [Optimal Junction Trees](https://mlsanity.com/paper/1302.6823/) (2013)
- [Accelerating Recursive Partition-Based Causal Structure Learning](https://mlsanity.com/paper/2102.11545/) (2021)

## Abstract (arXiv)

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.