# A Recursive Markov Boundary-Based Approach to Causal Structure Learning

arXiv: https://arxiv.org/abs/2010.04992 · HTML: https://mlsanity.com/paper/2010.04992/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2020.

## Built on by (most cited first, 21 of 21)

- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [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)
- [Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables](https://mlsanity.com/paper/2208.06935/) (2022)
- [Causal Effect Identification with Context-specific Independence Relations of Control Variables](https://mlsanity.com/paper/2110.12064/) (2021)
- [DCILP: A Distributed Approach for Large-Scale Causal Structure Learning](https://mlsanity.com/paper/2406.10481/) (2024)
- [A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models](https://mlsanity.com/paper/2205.10083/) (2022)
- [Scalable and Flexible Causal Discovery with an Efficient Test for Adjacency](https://mlsanity.com/paper/2406.09177/) (2024)
- [Efficient Ensemble Conditional Independence Test Framework for Causal Discovery](https://mlsanity.com/paper/2509.21021/) (2025)
- [Towards Practical Multi-label Causal Discovery in High-Dimensional Event Sequences via One-Shot Graph Aggregation](https://mlsanity.com/paper/2509.19112/) (2025)
- [s-ID: Causal Effect Identification in a Sub-Population](https://mlsanity.com/paper/2309.02281/) (2023)
- [Reinforcement Learning for Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2408.13448/) (2024)
- [SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graph](https://mlsanity.com/paper/2502.07857/) (2025)
- [Local Causal Discovery for Statistically Efficient Causal Inference](https://mlsanity.com/paper/2510.14582/) (2025)
- [QWO: Speeding Up Permutation-Based Causal Discovery in LiGAMs](https://mlsanity.com/paper/2410.23155/) (2024)
- [Learning Linear Gaussian Polytree Models with Interventions](https://mlsanity.com/paper/2311.04636/) (2023)
- [Design of Experiment for Discovering Directed Mixed Graph](https://mlsanity.com/paper/2509.01887/) (2025)
- [Efficient Causal Structure Learning via Modular Subgraph Integration](https://mlsanity.com/paper/2601.21014/) (2026)
- [Multi-Agent Causal Reasoning System for Error Pattern Rule Automation in Vehicles](https://mlsanity.com/paper/2602.01155/) (2026)
- [A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2605.10651/) (2026)
- [Decoupled Causal Discovery](https://mlsanity.com/paper/2609.23535/) (2026)

## Abstract (arXiv)

Constraint-based methods are one of the main approaches for causal structure learning that are particularly valued as they are asymptotically guaranteed to find a structure that is Markov equivalent to the causal graph of the system. On the other hand, they may require an exponentially large number of conditional independence (CI) tests in the number of variables of the system. In this paper, we propose a novel recursive constraint-based method for causal structure learning that significantly reduces the required number of CI tests compared to the existing literature. The idea of the proposed approach is to use Markov boundary information to identify a specific variable that can be removed from the set of variables without affecting the statistical dependencies among the other variables. Having identified such a variable, we discover its neighborhood, remove that variable from the set of variables, and recursively learn the causal structure over the remaining variables. We further provide a lower bound on the number of CI tests required by any constraint-based method. Comparing this lower bound to our achievable bound demonstrates the efficiency of the proposed approach. Our experimental results show that the proposed algorithm outperforms state-of-the-art both on synthetic and real-world structures.