# DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning

arXiv: https://arxiv.org/abs/2210.04389 · HTML: https://mlsanity.com/paper/2210.04389/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 69 references that are in the map.
- First posted on arXiv 10 Oct 2022.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Improving Reproducibility in Machine Learning Research (A Report from the NeurIPS 2019 Reproducibility Program)](https://mlsanity.com/paper/2003.12206/) (2020)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Deep Network Approximation for Smooth Functions](https://mlsanity.com/paper/2001.03040/) (2020)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Fair Inference On Outcomes](https://mlsanity.com/paper/1705.10378/) (2017)
- [Causal Machine Learning: A Survey and Open Problems](https://mlsanity.com/paper/2206.15475/) (2022)
- [Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1709.01953/) (2017)
- [Sharp Bounds on the Approximation Rates, Metric Entropy, and n-widths of Shallow Neural Networks](https://mlsanity.com/paper/2101.12365/) (2021)
- [It's COMPASlicated: The Messy Relationship between RAI Datasets and Algorithmic Fairness Benchmarks](https://mlsanity.com/paper/2106.05498/) (2021)
- [Superpolynomial Lower Bounds for Learning One-Layer Neural Networks using Gradient Descent](https://mlsanity.com/paper/2006.12011/) (2020)
- [The Surprising Simplicity of the Early-Time Learning Dynamics of Neural Networks](https://mlsanity.com/paper/2006.14599/) (2020)
- [The gap between theory and practice in function approximation with deep neural networks](https://mlsanity.com/paper/2001.07523/) (2020)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [Learning Deep ReLU Networks Is Fixed-Parameter Tractable](https://mlsanity.com/paper/2009.13512/) (2020)
- [On the Representation of Solutions to Elliptic PDEs in Barron Spaces](https://mlsanity.com/paper/2106.07539/) (2021)
- [A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects](https://mlsanity.com/paper/1903.03662/) (2019)
- [Estimation error analysis of deep learning on the regression problem on the variable exponent Besov space](https://mlsanity.com/paper/2009.11285/) (2020)
- [An Interventionist Approach to Mediation Analysis](https://mlsanity.com/paper/2008.06019/) (2020)
- [Proximal mediation analysis](https://mlsanity.com/paper/2109.11904/) (2021)
- [Selective machine learning of doubly robust functionals](https://mlsanity.com/paper/1911.02029/) (2019)
- [Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning](https://mlsanity.com/paper/2008.03288/) (2020)
- [Causal Inference of General Treatment Effects using Neural Networks with A Diverging Number of Confounders](https://mlsanity.com/paper/2009.07055/) (2020)
- [On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding](https://mlsanity.com/paper/1710.02011/) (2017)
- [Double-robust and efficient methods for estimating the causal effects of a binary treatment](https://mlsanity.com/paper/2008.00507/) (2020)

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

- [Causal Mediation Analysis with Multi-dimensional and Indirectly Observed Mediators](https://mlsanity.com/paper/2306.07918/) (2023)
- [On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models](https://mlsanity.com/paper/2606.22391/) (2026)
- [Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators](https://mlsanity.com/paper/2306.10590/) (2023)
- [New √n-consistent, numerically stable higher-order influence function estimators](https://mlsanity.com/paper/2302.08097/) (2023)
- [DNA-SE: Towards Deep Neural-Nets Assisted Semiparametric Estimation](https://mlsanity.com/paper/2408.02045/) (2024)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglement](https://mlsanity.com/paper/2509.22553/) (2025)
- [Decomposing Discrimination: Causal Mediation Analysis for AI-Driven Credit Decisions](https://mlsanity.com/paper/2603.27510/) (2026)
- [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 can unpack the black box of causality and is therefore a powerful tool for disentangling causal pathways in biomedical and social sciences, and also for evaluating machine learning fairness. To reduce bias for estimating Natural Direct and Indirect Effects in mediation analysis, we propose a new method called DeepMed that uses deep neural networks (DNNs) to cross-fit the infinite-dimensional nuisance functions in the efficient influence functions. We obtain novel theoretical results that our DeepMed method (1) can achieve semiparametric efficiency bound without imposing sparsity constraints on the DNN architecture and (2) can adapt to certain low dimensional structures of the nuisance functions, significantly advancing the existing literature on DNN-based semiparametric causal inference. Extensive synthetic experiments are conducted to support our findings and also expose the gap between theory and practice. As a proof of concept, we apply DeepMed to analyze two real datasets on machine learning fairness and reach conclusions consistent with previous findings.