Inference for Deep Neural Network Estimators in Generalized Nonparametric Models
This addresses the underexplored issue of inference for DNN estimators in generalized nonparametric models, providing a rigorous framework for clinical decision-making, though it is incremental as it builds on existing DNN methods with a novel inference approach.
The authors tackled the problem of performing statistical inference on deep neural network (DNN) estimates for categorical or exponential family outcomes in generalized nonparametric regression models, proposing an Ensemble Subsampling Method (ESM) that constructs reliable confidence intervals and demonstrates effectiveness in simulations and an eICU dataset application.
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.