# A Local Method for Identifying Causal Relations under Markov Equivalence

arXiv: https://arxiv.org/abs/2102.12685 · HTML: https://mlsanity.com/paper/2102.12685/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 69 references that are in the map.
- First posted on arXiv 25 Feb 2021.

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

- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Domain Adaptation as a Problem of Inference on Graphical Models](https://mlsanity.com/paper/2002.03278/) (2020)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cycles](https://mlsanity.com/paper/2005.00610/) (2020)
- [Ancestral Causal Inference](https://mlsanity.com/paper/1606.07035/) (2016)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Minimal enumeration of all possible total effects in a Markov equivalence class](https://mlsanity.com/paper/2010.08611/) (2020)
- [A generalized back-door criterion](https://mlsanity.com/paper/1307.5636/) (2013)
- [Testing Mediation Effects Using Logic of Boolean Matrices](https://mlsanity.com/paper/2005.04584/) (2020)

## Built on by (most cited first, 6 of 6)

- [Counterfactual Fairness with Partially Known Causal Graph](https://mlsanity.com/paper/2205.13972/) (2022)
- [Local Causal Discovery with Background Knowledge](https://mlsanity.com/paper/2408.07890/) (2024)
- [Local Causal Discovery for Statistically Efficient Causal Inference](https://mlsanity.com/paper/2510.14582/) (2025)
- [Towards Human-like Perception: Learning Structural Causal Model in Heterogeneous Graph](https://mlsanity.com/paper/2312.05757/) (2023)
- [Coordinated Multi-Neighborhood Learning on a Directed Acyclic Graph](https://mlsanity.com/paper/2405.15358/) (2024)
- [Integrating Background Knowledge for Scalable Causal Discovery](https://mlsanity.com/paper/2607.10456/) (2026)

## Abstract (arXiv)

Causality is important for designing interpretable and robust methods in artificial intelligence research. We propose a local approach to identify whether a variable is a cause of a given target under the framework of causal graphical models of directed acyclic graphs (DAGs). In general, the causal relation between two variables may not be identifiable from observational data as many causal DAGs encoding different causal relations are Markov equivalent. In this paper, we first introduce a sufficient and necessary graphical condition to check the existence of a causal path from a variable to a target in every Markov equivalent DAG. Next, we provide local criteria for identifying whether a variable is a cause/non-cause of a target based only on the local structure instead of the entire graph. Finally, we propose a local learning algorithm for this causal query via learning the local structure of the variable and some additional statistical independence tests related to the target. Simulation studies show that our local algorithm is efficient and effective, compared with other state-of-art methods.