# Minimal enumeration of all possible total effects in a Markov equivalence class

arXiv: https://arxiv.org/abs/2010.08611 · HTML: https://mlsanity.com/paper/2010.08611/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2020.

## Built on by (most cited first, 12 of 12)

- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Counterfactual Fairness with Partially Known Causal Graph](https://mlsanity.com/paper/2205.13972/) (2022)
- [Active causal structure learning with advice](https://mlsanity.com/paper/2305.19588/) (2023)
- [Do we become wiser with time? On causal equivalence with tiered background knowledge](https://mlsanity.com/paper/2306.01638/) (2023)
- [A Local Method for Identifying Causal Relations under Markov Equivalence](https://mlsanity.com/paper/2102.12685/) (2021)
- [Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach](https://mlsanity.com/paper/2401.10632/) (2024)
- [Local Causal Discovery with Background Knowledge](https://mlsanity.com/paper/2408.07890/) (2024)
- [Estimating Causal Effects in Partially Directed Parametric Causal Factor Graphs](https://mlsanity.com/paper/2411.07006/) (2024)
- [Practical Algorithms for Orientations of Partially Directed Graphical Models](https://mlsanity.com/paper/2302.14386/) (2023)
- [Mechanisms for Data Sharing in Collaborative Causal Inference (Extended Version)](https://mlsanity.com/paper/2407.11032/) (2024)
- [Estimate Collapsibility of Causal Effects in Completed Partial DAGs via Strong d-Convex Hulls](https://mlsanity.com/paper/2606.08941/) (2026)
- [Lifted Causal Inference](https://mlsanity.com/paper/2606.28024/) (2026)

## Abstract (arXiv)

In observational studies, when a total causal effect of interest is not identified, the set of all possible effects can be reported instead. This typically occurs when the underlying causal DAG is only known up to a Markov equivalence class, or a refinement thereof due to background knowledge. As such, the class of possible causal DAGs is represented by a maximally oriented partially directed acyclic graph (MPDAG), which contains both directed and undirected edges. We characterize the minimal additional edge orientations required to identify a given total effect. A recursive algorithm is then developed to enumerate subclasses of DAGs, such that the total effect in each subclass is identified as a distinct functional of the observed distribution. This resolves an issue with existing methods, which often report possible total effects with duplicates, namely those that are numerically distinct due to sampling variability but are in fact causally identical.