# Causal Identification under Markov Equivalence

arXiv: https://arxiv.org/abs/1812.06209 · HTML: https://mlsanity.com/paper/1812.06209/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2018.

## Built on by (most cited first, 15 of 15)

- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias](https://mlsanity.com/paper/2111.04095/) (2021)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Counterfactual Image Editing](https://mlsanity.com/paper/2403.09683/) (2024)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Membership Inference Attacks and Generalization: A Causal Perspective](https://mlsanity.com/paper/2209.08615/) (2022)
- [From Temporal to Contemporaneous Iterative Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2306.00624/) (2023)
- [Evaluation of Induced Expert Knowledge in Causal Structure Learning by NOTEARS](https://mlsanity.com/paper/2301.01817/) (2023)
- [Towards Bounding Causal Effects under Markov Equivalence](https://mlsanity.com/paper/2311.07259/) (2023)
- [Finding and Listing Front-door Adjustment Sets](https://mlsanity.com/paper/2210.05816/) (2022)
- [Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimand](https://mlsanity.com/paper/2402.07419/) (2024)
- [Benchmarks for Reinforcement Learning with Biased Offline Data and Imperfect Simulators](https://mlsanity.com/paper/2407.00806/) (2024)
- [Representation Disentaglement via Regularization by Causal Identification](https://mlsanity.com/paper/2303.00128/) (2023)
- [CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery](https://mlsanity.com/paper/2607.01936/) (2026)

## Abstract (arXiv)

Assessing the magnitude of cause-and-effect relations is one of the central challenges found throughout the empirical sciences. The problem of identification of causal effects is concerned with determining whether a causal effect can be computed from a combination of observational data and substantive knowledge about the domain under investigation, which is formally expressed in the form of a causal graph. In many practical settings, however, the knowledge available for the researcher is not strong enough so as to specify a unique causal graph. Another line of investigation attempts to use observational data to learn a qualitative description of the domain called a Markov equivalence class, which is the collection of causal graphs that share the same set of observed features. In this paper, we marry both approaches and study the problem of causal identification from an equivalence class, represented by a partial ancestral graph (PAG). We start by deriving a set of graphical properties of PAGs that are carried over to its induced subgraphs. We then develop an algorithm to compute the effect of an arbitrary set of variables on an arbitrary outcome set. We show that the algorithm is strictly more powerful than the current state of the art found in the literature.