# Dimension-Free Average Treatment Effect Inference with Deep Neural Networks

arXiv: https://arxiv.org/abs/2112.01574 · HTML: https://mlsanity.com/paper/2112.01574/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 2 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)

## Built on by (most cited first, 3 of 3)

- [Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regression](https://mlsanity.com/paper/2207.09139/) (2022)
- [Factor Informed Double Deep Learning For Average Treatment Effect Estimation](https://mlsanity.com/paper/2508.17136/) (2025)
- [BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect](https://mlsanity.com/paper/2211.10793/) (2022)

## Abstract (arXiv)

This paper investigates the estimation and inference of the average treatment effect (ATE) using deep neural networks (DNNs) in the potential outcomes framework. Under some regularity conditions, the observed response can be formulated as the response of a mean regression problem with both the confounding variables and the treatment indicator as the independent variables. Using such formulation, we investigate two methods for ATE estimation and inference based on the estimated mean regression function via DNN regression using a specific network architecture. We show that both DNN estimates of ATE are consistent with dimension-free consistency rates under some assumptions on the underlying true mean regression model. Our model assumptions accommodate the potentially complicated dependence structure of the observed response on the covariates, including latent factors and nonlinear interactions between the treatment indicator and confounding variables. We also establish the asymptotic normality of our estimators based on the idea of sample splitting, ensuring precise inference and uncertainty quantification. Simulation studies and real data application justify our theoretical findings and support our DNN estimation and inference methods.