# Causal Mediation Analysis with Multi-dimensional and Indirectly Observed Mediators

arXiv: https://arxiv.org/abs/2306.07918 · HTML: https://mlsanity.com/paper/2306.07918/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 13 Jun 2023.

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

- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [The State of Applied Econometrics - Causality and Policy Evaluation](https://mlsanity.com/paper/1607.00699/) (2016)
- [Counterfactuals and Policy Analysis in Structural Models](https://mlsanity.com/paper/1302.4929/) (2013)
- [Causal Mediation Analysis with Hidden Confounders](https://mlsanity.com/paper/2102.11724/) (2021)
- [DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning](https://mlsanity.com/paper/2210.04389/) (2022)
- [Disentangled Representation for Causal Mediation Analysis](https://mlsanity.com/paper/2302.09694/) (2023)
- [Estimating Causal Effects using a Multi-task Deep Ensemble](https://mlsanity.com/paper/2301.11351/) (2023)
- [High-dimensional Multivariate Mediation: with Application to Neuroimaging Data](https://mlsanity.com/paper/1511.09354/) (2015)

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

- [Deep Causal Inference for Point-referenced Spatial Data with Continuous Treatments](https://mlsanity.com/paper/2412.04285/) (2024)
- [Estimating Treatment Effects with Independent Component Analysis](https://mlsanity.com/paper/2507.16467/) (2025)
- [MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysis](https://mlsanity.com/paper/2606.30648/) (2026)
- [AI-driven Multimodal Representation Learning for Latent Mediation Structure Discovery of Socioeconomic Disadvantage, Psychosocial Factors, and Cardiometabolic Multimorbidity: Insights from the All of Us Research Program](https://mlsanity.com/paper/2608.04016/) (2026)

## Abstract (arXiv)

Causal mediation analysis (CMA) is a powerful method to dissect the total effect of a treatment into direct and mediated effects within the potential outcome framework. This is important in many scientific applications to identify the underlying mechanisms of a treatment effect. However, in many scientific applications the mediator is unobserved, but there may exist related measurements. For example, we may want to identify how changes in brain activity or structure mediate an antidepressant's effect on behavior, but we may only have access to electrophysiological or imaging brain measurements. To date, most CMA methods assume that the mediator is one-dimensional and observable, which oversimplifies such real-world scenarios. To overcome this limitation, we introduce a CMA framework that can handle complex and indirectly observed mediators based on the identifiable variational autoencoder (iVAE) architecture. We prove that the true joint distribution over observed and latent variables is identifiable with the proposed method. Additionally, our framework captures a disentangled representation of the indirectly observed mediator and yields accurate estimation of the direct and mediated effects in synthetic and semi-synthetic experiments, providing evidence of its potential utility in real-world applications.