# Finding and Listing Front-door Adjustment Sets

arXiv: https://arxiv.org/abs/2210.05816 · HTML: https://mlsanity.com/paper/2210.05816/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 46 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 7 of 7)

- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework](https://mlsanity.com/paper/1803.00116/) (2018)
- [Causal Identification under Markov Equivalence](https://mlsanity.com/paper/1812.06209/) (2018)
- [Efficient adjustment sets in causal graphical models with hidden variables](https://mlsanity.com/paper/2004.10521/) (2020)
- [Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge](https://mlsanity.com/paper/2106.11560/) (2021)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)

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

- [Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder](https://mlsanity.com/paper/2310.01937/) (2023)
- [Linear-Time Algorithms for Front-Door Adjustment in Causal Graphs](https://mlsanity.com/paper/2211.16468/) (2022)
- [Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge](https://mlsanity.com/paper/2306.11008/) (2023)
- [Causal Effect Estimation with Variational AutoEncoder and the Front Door Criterion](https://mlsanity.com/paper/2304.11969/) (2023)
- [Linear-Time Primitives for Algorithm Development in Graphical Causal Inference](https://mlsanity.com/paper/2506.15758/) (2025)
- [PIPCFR: Pseudo-outcome Imputation with Post-treatment Variables for Individual Treatment Effect Estimation](https://mlsanity.com/paper/2512.18737/) (2025)

## Abstract (arXiv)

Identifying the effects of new interventions from data is a significant challenge found across a wide range of the empirical sciences. A well-known strategy for identifying such effects is Pearl's front-door (FD) criterion (Pearl, 1995). The definition of the FD criterion is declarative, only allowing one to decide whether a specific set satisfies the criterion. In this paper, we present algorithms for finding and enumerating possible sets satisfying the FD criterion in a given causal diagram. These results are useful in facilitating the practical applications of the FD criterion for causal effects estimation and helping scientists to select estimands with desired properties, e.g., based on cost, feasibility of measurement, or statistical power.