# Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks

arXiv: https://arxiv.org/abs/2505.01995 · HTML: https://mlsanity.com/paper/2505.01995/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 71 references that are in the map.
- First posted on arXiv 4 May 2025.

## Builds on (most cited first, 28 of 28)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Optimal approximation of piecewise smooth functions using deep ReLU neural networks](https://mlsanity.com/paper/1709.05289/) (2017)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Minimum Width for Universal Approximation](https://mlsanity.com/paper/2006.08859/) (2020)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Approximation with Sparsely Connected Deep Neural Networks](https://mlsanity.com/paper/1705.01714/) (2017)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Consistent Sparse Deep Learning: Theory and Computation](https://mlsanity.com/paper/2102.13229/) (2021)
- [Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods](https://mlsanity.com/paper/1701.05306/) (2017)
- [An Adaptive Empirical Bayesian Method for Sparse Deep Learning](https://mlsanity.com/paper/1910.10791/) (2019)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Minimum width for universal approximation using ReLU networks on compact domain](https://mlsanity.com/paper/2309.10402/) (2023)
- [Assessing Treatment Effect Variation in Observational Studies: Results from a Data Challenge](https://mlsanity.com/paper/1907.07592/) (2019)
- [Singular Values for ReLU Layers](https://mlsanity.com/paper/1812.02566/) (2018)
- [Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network](https://mlsanity.com/paper/2210.04349/) (2022)
- [A Kernel-Expanded Stochastic Neural Network](https://mlsanity.com/paper/2201.05319/) (2022)
- [Extended Stochastic Gradient MCMC for Large-Scale Bayesian Variable Selection](https://mlsanity.com/paper/2002.02919/) (2020)
- [Generalized Fiducial Inference on Differentiable Manifolds](https://mlsanity.com/paper/2209.15473/) (2022)
- [Extended Fiducial Inference: Toward an Automated Process of Statistical Inference](https://mlsanity.com/paper/2407.21622/) (2024)
- [Markov Neighborhood Regression for High-Dimensional Inference](https://mlsanity.com/paper/2010.08864/) (2020)

## Built on by (most cited first, 1 of 1)

- [Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inference](https://mlsanity.com/paper/2505.19136/) (2025)

## Abstract (arXiv)

Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial inference (EFI). In the proposed method, deep neural networks are used to model the treatment and control effect functions, while an additional neural network is employed to estimate their parameters. The universal approximation capability of deep neural networks ensures the broad applicability of this method. Numerical results highlight the superior performance of the proposed Double-NN method compared to the conformal quantile regression (CQR) method in individual treatment effect estimation. From the perspective of statistical inference, this work advances the theory and methodology for statistical inference of large models. Specifically, it is theoretically proven that the proposed method permits the model size to increase with the sample size n at a rate of O(nzeta) for some 0 ≤ zeta<1, while still maintaining proper quantification of uncertainty in the model parameters. This result marks a significant improvement compared to the range 0≤ zeta < frac12 required by the classical central limit theorem. Furthermore, this work provides a rigorous framework for quantifying the uncertainty of deep neural networks under the neural scaling law, representing a substantial contribution to the statistical understanding of large-scale neural network models.