# Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge

arXiv: https://arxiv.org/abs/2306.11008 · HTML: https://mlsanity.com/paper/2306.11008/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 45 references that are in the map.
- First posted on arXiv 19 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Learning Optimal Fair Policies](https://mlsanity.com/paper/1809.02244/) (2018)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Causal Fairness Analysis](https://mlsanity.com/paper/2207.11385/) (2022)
- [Learning and Testing Causal Models with Interventions](https://mlsanity.com/paper/1805.09697/) (2018)
- [Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding](https://mlsanity.com/paper/2003.01747/) (2020)
- [Efficient Intervention Design for Causal Discovery with Latents](https://mlsanity.com/paper/2005.11736/) (2020)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge](https://mlsanity.com/paper/2106.11560/) (2021)
- [Estimating and Controlling the False Discovery Rate for the PC Algorithm Using Edge-Specific P-Values](https://mlsanity.com/paper/1607.03975/) (2016)
- [Estimating Treatment Effects with Observed Confounders and Mediators](https://mlsanity.com/paper/2003.11991/) (2020)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [Finding and Listing Front-door Adjustment Sets](https://mlsanity.com/paper/2210.05816/) (2022)
- [Differentiable Causal Backdoor Discovery](https://mlsanity.com/paper/2003.01461/) (2020)

## Built on by (most cited first, 4 of 4)

- [Cross-modal Causal Relation Alignment for Video Question Grounding](https://mlsanity.com/paper/2503.07635/) (2025)
- [Local Causal Discovery for Structural Evidence of Direct Discrimination](https://mlsanity.com/paper/2405.14848/) (2024)
- [Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models](https://mlsanity.com/paper/2405.14496/) (2024)
- [Mitigating Hidden Confounding by Progressive Confounder Imputation via Large Language Models](https://mlsanity.com/paper/2507.02928/) (2025)

## Abstract (arXiv)

Causal effect estimation from data typically requires assumptions about the cause-effect relations either explicitly in the form of a causal graph structure within the Pearlian framework, or implicitly in terms of (conditional) independence statements between counterfactual variables within the potential outcomes framework. When the treatment variable and the outcome variable are confounded, front-door adjustment is an important special case where, given the graph, causal effect of the treatment on the target can be estimated using post-treatment variables. However, the exact formula for front-door adjustment depends on the structure of the graph, which is difficult to learn in practice. In this work, we provide testable conditional independence statements to compute the causal effect using front-door-like adjustment without knowing the graph under limited structural side information. We show that our method is applicable in scenarios where knowing the Markov equivalence class is not sufficient for causal effect estimation. We demonstrate the effectiveness of our method on a class of random graphs as well as real causal fairness benchmarks.