# On Testability of the Front-Door Model via Verma Constraints

arXiv: https://arxiv.org/abs/2203.00161 · HTML: https://mlsanity.com/paper/2203.00161/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 1 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [On the Testability of Causal Models with Latent and Instrumental Variables](https://mlsanity.com/paper/1302.4976/) (2013)
- [Margins of discrete Bayesian networks](https://mlsanity.com/paper/1501.02103/) (2015)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [Fast Conditional Independence Test for Vector Variables with Large Sample Sizes](https://mlsanity.com/paper/1804.02747/) (2018)
- [Markovian acyclic directed mixed graphs for discrete data](https://mlsanity.com/paper/1301.6624/) (2013)
- [Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge](https://mlsanity.com/paper/2106.11560/) (2021)
- [Multivariate Counterfactual Systems And Causal Graphical Models](https://mlsanity.com/paper/2008.06017/) (2020)
- [Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs](https://mlsanity.com/paper/1302.1566/) (2013)
- [Statistical Testing under Distributional Shifts](https://mlsanity.com/paper/2105.10821/) (2021)
- [On falsification of the binary instrumental variable model](https://mlsanity.com/paper/1605.03677/) (2016)
- [Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables](https://mlsanity.com/paper/2107.07087/) (2021)

## Built on by (most cited first, 8 of 8)

- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [RCT Rejection Sampling for Causal Estimation Evaluation](https://mlsanity.com/paper/2307.15176/) (2023)
- [Proximal Causal Inference With Text Data](https://mlsanity.com/paper/2401.06687/) (2024)
- [Latent Variable Causal Discovery under Selection Bias](https://mlsanity.com/paper/2512.11219/) (2025)
- [Finding and Listing Front-door Adjustment Sets](https://mlsanity.com/paper/2210.05816/) (2022)
- [Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge](https://mlsanity.com/paper/2306.11008/) (2023)
- [Robust Weighted Triangulation of Causal Effects Under Model Uncertainty](https://mlsanity.com/paper/2603.01119/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)

## Abstract (arXiv)

The front-door criterion can be used to identify and compute causal effects despite the existence of unmeasured confounders between a treatment and outcome. However, the key assumptions -- (i) the existence of a variable (or set of variables) that fully mediates the effect of the treatment on the outcome, and (ii) which simultaneously does not suffer from similar issues of confounding as the treatment-outcome pair -- are often deemed implausible. This paper explores the testability of these assumptions. We show that under mild conditions involving an auxiliary variable, the assumptions encoded in the front-door model (and simple extensions of it) may be tested via generalized equality constraints a.k.a Verma constraints. We propose two goodness-of-fit tests based on this observation, and evaluate the efficacy of our proposal on real and synthetic data. We also provide theoretical and empirical comparisons to instrumental variable approaches to handling unmeasured confounding.