# Proximal Mediation Analysis with Hidden Recanting Witnesses

arXiv: https://arxiv.org/abs/2606.17600 · HTML: https://mlsanity.com/paper/2606.17600/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 47 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Builds on (most cited first, 25 of 25)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Learning Optimal Fair Policies](https://mlsanity.com/paper/1809.02244/) (2018)
- [A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2111.06784/) (2021)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Proximal Causal Inference for Complex Longitudinal Studies](https://mlsanity.com/paper/2109.07030/) (2021)
- [Proximal mediation analysis](https://mlsanity.com/paper/2109.11904/) (2021)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding](https://mlsanity.com/paper/1710.02011/) (2017)
- [Causal Inference with Hidden Mediators](https://mlsanity.com/paper/2111.02927/) (2021)
- [Proximal Causal Inference for Marginal Counterfactual Survival Curves](https://mlsanity.com/paper/2204.13144/) (2022)
- [Proximal Survival Analysis to Handle Dependent Right Censoring](https://mlsanity.com/paper/2208.07014/) (2022)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Causal Inference with a Hidden Treatment](https://mlsanity.com/paper/2405.09080/) (2024)
- [Blessing from Human-AI Interaction: Super Reinforcement Learning in Confounded Environments](https://mlsanity.com/paper/2209.15448/) (2022)
- [Adaptive Proximal Causal Inference with Some Invalid Proxies](https://mlsanity.com/paper/2507.19623/) (2025)
- [On Identification of Optimal Dynamic Treatment Regimes with Proxies of Hidden Confounders](https://mlsanity.com/paper/2402.14942/) (2024)
- [Fortified Proximal Causal Inference with Many Invalid Proxies](https://mlsanity.com/paper/2506.13152/) (2025)
- [On Multiple Robustness of Proximal Dynamic Treatment Regimes](https://mlsanity.com/paper/2510.20451/) (2025)
- [Double Fairness Policy Learning: Integrating Action Fairness and Outcome Fairness in Decision-making](https://mlsanity.com/paper/2601.19186/) (2026)
- [Proximal Causal Inference for Hidden Outcomes](https://mlsanity.com/paper/2605.09849/) (2026)
- [Proximal Path-Specific Inference](https://mlsanity.com/paper/2605.09462/) (2026)

## Abstract (arXiv)

Mediation analysis is essential for decomposing the causal effect of a treatment into direct and indirect pathways. However, many practical settings rely on the stringent assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori. Such a requirement is often untenable, especially when these variables remain unobservable due to measurement difficulties or privacy constraints. In this paper, we leverage proximal causal inference to develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses. Building on this, we develop a semiparametric inference framework that derives the efficient influence function and proposes a proximal multiply robust estimator, which remains consistent if at least one set of nuisance models is correctly specified. When all nuisance models are correctly specified and converge at appropriate rates, the estimator is asymptotically normal and achieves the semiparametric efficiency bound. We provide a minimax optimization-based debiased machine learning procedure for point estimation and constructing valid confidence intervals. The performance of the proposed methods is demonstrated by simulation studies and a real data application.