Inference for Deep Neural Network Estimators in Generalized Nonparametric Models.

Area of Science:

• Machine Learning
• Statistical Inference
• Biostatistics

Background:

• Deep neural networks (DNNs) are widely used for prediction, but statistical inference on their outputs for categorical or exponential family outcomes is challenging.
• Existing methods often rely on assumptions of independence between estimation errors and inputs, which are frequently violated in generalized nonparametric regression models (GNRMs).
• This gap limits the application of DNNs in scenarios requiring rigorous uncertainty quantification for subject-specific predictions.

Purpose of the Study:

• To propose a novel DNN estimator tailored for GNRMs, facilitating robust statistical inference.
• To develop a theoretical framework that allows for dependence between estimation errors and inputs, addressing limitations of prior work.
• To introduce a practical inference method, the Ensemble Subsampling Method (ESM), for constructing reliable confidence intervals for DNN-based predictions.

Main Methods:

• Developed a DNN estimator within the framework of GNRMs, explicitly accounting for potential dependence structures.
• Proposed the Ensemble Subsampling Method (ESM), utilizing U-statistics and Hoeffding decomposition for variance estimation.
• Validated the method through simulations on nonparametric logistic, Poisson, and binomial regression models and applied it to the eICU dataset.

Main Results:

• The proposed DNN estimator and inference framework are theoretically sound and feasible under GNRM settings, even with dependent errors.
• ESM demonstrated model-free variance estimation and effective handling of population heterogeneity, yielding reliable confidence intervals.
• The method showed effectiveness and efficiency in simulations and provided valuable patient-centric insights when applied to ICU readmission risk prediction.

Conclusions:

• This work bridges the gap between DNN prediction and rigorous statistical inference for complex outcome types.
• The proposed approach and ESM offer a powerful tool for uncertainty quantification in DNN-based predictions within GNRMs.
• The findings have significant implications for clinical decision-making, exemplified by the successful prediction of ICU readmission risk.