# Inference for Deep Neural Network Estimators in Generalized Nonparametric Models

arXiv: https://arxiv.org/abs/2504.09347 · HTML: https://mlsanity.com/paper/2504.09347/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 12 Apr 2025.

## Builds on (most cited first, 9 of 9)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Benign Overfitting in Two-layer Convolutional Neural Networks](https://mlsanity.com/paper/2202.06526/) (2022)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Nonlinear Approximation via Compositions](https://mlsanity.com/paper/1902.10170/) (2019)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [The HulC: Confidence Regions from Convex Hulls](https://mlsanity.com/paper/2105.14577/) (2021)

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

- [Beyond Consistency: Inference for the Relative risk functional in Deep Nonparametric Cox Models](https://mlsanity.com/paper/2603.23835/) (2026)
- [Prediction Inference of Time Series with Standard ReLU Deep Neural Networks](https://mlsanity.com/paper/2608.15362/) (2026)
- [Can Tabular Foundation Models Amortize Statistical Inference?](https://mlsanity.com/paper/2609.33114/) (2026)

## Abstract (arXiv)

While deep neural networks (DNNs) are used for prediction, inference on DNN-estimated subject-specific means for categorical or exponential family outcomes remains underexplored. We address this by proposing a DNN estimator under generalized nonparametric regression models (GNRMs) and developing a rigorous inference framework. Unlike existing approaches that assume independence between estimation errors and inputs to establish the error bound, a condition often violated in GNRMs, we allow for dependence and our theoretical analysis demonstrates the feasibility of drawing inference under GNRMs. To implement inference, we consider an Ensemble Subsampling Method (ESM) that leverages U-statistics and the Hoeffding decomposition to construct reliable confidence intervals for DNN estimates. We show that, under GNRM settings, ESM enables model-free variance estimation and accounts for heterogeneity among individuals in the population. Through simulations under nonparametric logistic, Poisson, and binomial regression models, we demonstrate the effectiveness and efficiency of our method. We further apply the method to the electronic Intensive Care Unit (eICU) dataset, a large scale collection of anonymized health records from ICU patients, to predict ICU readmission risk and offer patient-centric insights for clinical decision making.