# Local Causal Structure Learning in the Presence of Latent Variables

arXiv: https://arxiv.org/abs/2405.16225 · HTML: https://mlsanity.com/paper/2405.16225/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 67 references that are in the map.
- First posted on arXiv 25 May 2024.

## Builds on (most cited first, 15 of 15)

- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [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)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [Local Constraint-Based Causal Discovery under Selection Bias](https://mlsanity.com/paper/2203.01848/) (2022)
- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables](https://mlsanity.com/paper/2208.06935/) (2022)
- [Discovery and inference of a causal network with hidden confounding](https://mlsanity.com/paper/2309.09420/) (2023)
- [Towards Efficient Local Causal Structure Learning](https://mlsanity.com/paper/2103.00378/) (2021)

## Built on by (most cited first, 11 of 11)

- [Local Causal Discovery with Background Knowledge](https://mlsanity.com/paper/2408.07890/) (2024)
- [One-Shot Multi-Label Causal Discovery in High-Dimensional Event Sequences](https://mlsanity.com/paper/2509.23213/) (2025)
- [Local Learning for Covariate Selection in Nonparametric Causal Effect Estimation with Latent Variables](https://mlsanity.com/paper/2411.16315/) (2024)
- [Local Causal Discovery for Statistically Efficient Causal Inference](https://mlsanity.com/paper/2510.14582/) (2025)
- [Order-based Rehearsal Learning](https://mlsanity.com/paper/2605.04955/) (2026)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects](https://mlsanity.com/paper/2505.02781/) (2025)
- [From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables](https://mlsanity.com/paper/2604.22416/) (2026)
- [A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2605.10651/) (2026)
- [Local Covariate Selection for Average Causal Effect Estimation without Pretreatment and Causal Sufficiency Assumptions](https://mlsanity.com/paper/2605.21548/) (2026)
- [seq2cause: One Autoregressive Backbone, Four Causal Discovery Tasks in Event Sequences](https://mlsanity.com/paper/2609.31801/) (2026)

## Abstract (arXiv)

Discovering causal relationships from observational data, particularly in the presence of latent variables, poses a challenging problem. While current local structure learning methods have proven effective and efficient when the focus lies solely on the local relationships of a target variable, they operate under the assumption of causal sufficiency. This assumption implies that all the common causes of the measured variables are observed, leaving no room for latent variables. Such a premise can be easily violated in various real-world applications, resulting in inaccurate structures that may adversely impact downstream tasks. In light of this, our paper delves into the primary investigation of locally identifying potential parents and children of a target from observational data that may include latent variables. Specifically, we harness the causal information from m-separation and V-structures to derive theoretical consistency results, effectively bridging the gap between global and local structure learning. Together with the newly developed stop rules, we present a principled method for determining whether a variable is a direct cause or effect of a target. Further, we theoretically demonstrate the correctness of our approach under the standard causal Markov and faithfulness conditions, with infinite samples. Experimental results on both synthetic and real-world data validate the effectiveness and efficiency of our approach.