# A generalized back-door criterion

arXiv: https://arxiv.org/abs/1307.5636 · HTML: https://mlsanity.com/paper/1307.5636/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2013.

## Built on by (most cited first, 9 of 9)

- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Identifiability of total effects from abstractions of time series causal graphs](https://mlsanity.com/paper/2310.14691/) (2023)
- [A Local Method for Identifying Causal Relations under Markov Equivalence](https://mlsanity.com/paper/2102.12685/) (2021)
- [Towards identifiability of micro total effects in summary causal graphs with latent confounding: extension of the front-door criterion](https://mlsanity.com/paper/2406.05805/) (2024)
- [Identifying Macro Causal Effects in a C-DMG over ADMGs](https://mlsanity.com/paper/2504.01551/) (2025)
- [Identifying Macro Causal Effects in C-DMGs over DMGs](https://mlsanity.com/paper/2506.19650/) (2025)
- [Causal reasoning in difference graphs](https://mlsanity.com/paper/2411.01292/) (2024)
- [Identifiability by common backdoor in summary causal graphs of time series](https://mlsanity.com/paper/2506.14862/) (2025)
- [Average Controlled and Average Natural Micro Direct Effects in Summary Causal Graphs](https://mlsanity.com/paper/2410.23975/) (2024)

## Abstract (arXiv)

We generalize Pearl's back-door criterion for directed acyclic graphs (DAGs) to more general types of graphs that describe Markov equivalence classes of DAGs and/or allow for arbitrarily many hidden variables. We also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back-door criterion, when considering a single intervention and a single outcome variable. Moreover, if such a set exists, we provide an explicit set that fulfills the criterion. We illustrate the results in several examples. R-code is available in the R-package pcalg.