为深度神经网络估计的个体均值提供可靠推断方法，适用于各类非参数回归模型。
Inference for Deep Neural Network Estimators in Generalized Nonparametric Models
- 提出基于广义非参数回归模型的DNN估计器，允许估计误差与输入相关。
- 通过集成抽样法构建置信区间，在模拟和真实医疗数据中表现良好。
- 适用于临床决策支持，可个性化预测重症患者再入院风险。
尽管深度神经网络广泛用于预测，但针对分类或指数族结果的DNN估计个体特定均值的推断研究仍不充分。本文提出一种在广义非参数回归模型（GNRM）下的DNN估计器，并建立严谨的推断框架。不同于现有方法假设估计误差与输入独立（该条件在GNRM中常不成立），本文允许两者依赖，理论分析证明了在GNRM下进行推断的可行性。为实现推断，引入集成抽样法（ESM），利用U统计量和Hoeffding分解构造可靠的置信区间。结果表明，在GNRM设定下，ESM可实现模型无关的方差估计，并捕捉人群中的个体异质性。通过非参数逻辑、泊松及二项回归模型的模拟验证了方法的有效性与高效性。进一步应用于大型电子重症监护数据库（eICU），对重症患者再入院风险进行预测，为临床决策提供个体化洞察。
原文摘要 · Abstract (English)
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.
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