# Causal Mediation Analysis with Hidden Confounders

arXiv: https://arxiv.org/abs/2102.11724 · HTML: https://mlsanity.com/paper/2102.11724/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 67 references that are in the map.
- First posted on arXiv 21 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [A Survey of Learning Causality with Data: Problems and Methods](https://mlsanity.com/paper/1809.09337/) (2018)
- [Counterfactual Risk Minimization: Learning from Logged Bandit Feedback](https://mlsanity.com/paper/1502.02362/) (2015)
- [Edward: A library for probabilistic modeling, inference, and criticism](https://mlsanity.com/paper/1610.09787/) (2016)
- [The Identification and Estimation of Direct and Indirect Effects in A/B Tests through Causal Mediation Analysis](https://mlsanity.com/paper/1906.09757/) (2019)
- [Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting](https://mlsanity.com/paper/1707.09021/) (2017)

## Built on by (most cited first, 10 of 10)

- [Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder](https://mlsanity.com/paper/2310.01937/) (2023)
- [Disentangled Representation for Causal Mediation Analysis](https://mlsanity.com/paper/2302.09694/) (2023)
- [Mitigating Propensity Bias of Large Language Models for Recommender Systems](https://mlsanity.com/paper/2409.20052/) (2024)
- [Causal Contrastive Learning for Counterfactual Regression Over Time](https://mlsanity.com/paper/2406.00535/) (2024)
- [Causal Mediation Analysis with Multi-dimensional and Indirectly Observed Mediators](https://mlsanity.com/paper/2306.07918/) (2023)
- [Causal Inference with Latent Variables: Recent Advances and Future Prospectives](https://mlsanity.com/paper/2406.13966/) (2024)
- [Causal Effect Estimation with Variational AutoEncoder and the Front Door Criterion](https://mlsanity.com/paper/2304.11969/) (2023)
- [Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Data](https://mlsanity.com/paper/2310.10559/) (2023)
- [M-learner:A Flexible And Powerful Framework To Study Heterogeneous Treatment Effect In Mediation Model](https://mlsanity.com/paper/2505.17917/) (2025)
- [CoSToM:Causal-oriented Steering for Intrinsic Theory-of-Mind Alignment in Large Language Models](https://mlsanity.com/paper/2604.10031/) (2026)

## Abstract (arXiv)

An important problem in causal inference is to break down the total effect of a treatment on an outcome into different causal pathways and to quantify the causal effect in each pathway. For instance, in causal fairness, the total effect of being a male employee (i.e., treatment) constitutes its direct effect on annual income (i.e., outcome) and the indirect effect via the employee's occupation (i.e., mediator). Causal mediation analysis (CMA) is a formal statistical framework commonly used to reveal such underlying causal mechanisms. One major challenge of CMA in observational studies is handling confounders, variables that cause spurious causal relationships among treatment, mediator, and outcome. Conventional methods assume sequential ignorability that implies all confounders can be measured, which is often unverifiable in practice. This work aims to circumvent the stringent sequential ignorability assumptions and consider hidden confounders. Drawing upon proxy strategies and recent advances in deep learning, we propose to simultaneously uncover the latent variables that characterize hidden confounders and estimate the causal effects. Empirical evaluations using both synthetic and semi-synthetic datasets validate the effectiveness of the proposed method. We further show the potentials of our approach for causal fairness analysis.