# MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysis

arXiv: https://arxiv.org/abs/2606.30648 · HTML: https://mlsanity.com/paper/2606.30648/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 5 Jun 2026.

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

- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning](https://mlsanity.com/paper/2210.04389/) (2022)
- [Factor-Adjusted Regularized Model Selection](https://mlsanity.com/paper/1612.08490/) (2016)
- [Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors](https://mlsanity.com/paper/1908.01252/) (2019)
- [Causal Mediation Analysis with Multi-dimensional and Indirectly Observed Mediators](https://mlsanity.com/paper/2306.07918/) (2023)
- [Multimodal hierarchical Variational AutoEncoders with Factor Analysis latent space](https://mlsanity.com/paper/2207.09185/) (2022)
- [Optimal Estimation of Large-Dimensional Nonlinear Factor Models](https://mlsanity.com/paper/2311.07243/) (2023)
- [Factor Informed Double Deep Learning For Average Treatment Effect Estimation](https://mlsanity.com/paper/2508.17136/) (2025)
- [Pathway Lasso: Estimate and Select Sparse Mediation Pathways with High Dimensional Mediators](https://mlsanity.com/paper/1603.07749/) (2016)
- [Statistical Inference for Linear Mediation Models with High-dimensional Mediators and Application to Studying Stock Reaction to COVID-19 Pandemic](https://mlsanity.com/paper/2108.12329/) (2021)
- [Causal Mediation Analysis: Selection with Asymptotically Valid Inference](https://mlsanity.com/paper/2110.06127/) (2021)
- [Statistical Inference in High-dimensional Poisson Regression with Applications to Mediation Analysis](https://mlsanity.com/paper/2410.20671/) (2024)
- [Debiased Causal Mediation Analysis in Ultra-High-Dimensional Settings in the Presence of Interaction Effects](https://mlsanity.com/paper/2412.08827/) (2024)

## Abstract (arXiv)

Causal mediation analysis decomposes a treatment effect into indirect pathways through mediators and direct pathways not operating through them. Modern biomedical studies often involve high-dimensional covariates and mediators that are noisy proxies for lower-dimensional latent biological processes. Existing methods typically rely on sparsity, linear factor models, or ignore the connection among variables in the learned representations, which can be restrictive when measurements are nonlinear and covariate and mediator factors are structurally dependent. We propose MediEncoder, a representation-learning framework for nonlinear high-dimensional mediation analysis. MediEncoder jointly learns low-dimensional covariate and mediator representations using a coupled encoder-decoder architecture with a cross-factor network that links treatment and covariate representations to mediator representations. The learned features are then used in a cross-fitted efficient influence function-based estimator of natural direct and indirect effects. The resulting estimator is multiply robust and asymptotically normal under suitable regularity conditions. Simulations show that MediEncoder improves estimation accuracy over competing dimension-reduction approaches, and an application to Alzheimer's Disease Neuroimaging Initiative data illustrates its utility in high-dimensional biomedical causal mediation analysis.