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.

翻译：尽管深度神经网络（DNNs）被广泛用于预测，但对于分类或指数族分布结果，基于DNN估计的个体特异性均值进行推断的研究仍然不足。为此，我们提出了一种在广义非参数回归模型（GNRMs）下的DNN估计量，并建立了一个严谨的推断框架。现有方法通常假设估计误差与输入之间相互独立以建立误差界，这一条件在GNRMs中常被违反；与之不同，我们允许依赖关系存在，并且理论分析证明了在GNRMs下进行推断的可行性。为实现推断，我们考虑了一种集成子抽样方法（ESM），该方法利用U统计量和Hoeffding分解为DNN估计构建可靠的置信区间。我们证明，在GNRM设定下，ESM能够实现无需模型假设的方差估计，并能够解释人群中个体间的异质性。通过在非参数逻辑回归、泊松回归和二项回归模型下的模拟实验，我们展示了该方法的有效性和效率。我们进一步将该方法应用于电子重症监护病房（eICU）数据集——一个来自ICU患者的大规模匿名健康记录集合，以预测ICU再入院风险，并为临床决策提供以患者为中心的见解。