用外部数据提升病例对照模型精度，实现最优非参数估计。
Deep non-parametric logistic model with case-control data and external summary information
- 结合外部汇总信息修正病例比例，改进非参数逻辑回归建模
- 提出两步法：先估比例，再加权训练深度网络，误差收敛率达最优
- 理论证明误差界并验证于模拟与真实数据，适合高维不平衡数据
病例对照抽样设计是缓解二分类数据不平衡的重要策略。本文研究在补充外部汇总信息的情况下，对非参数逻辑回归模型进行估计。外部信息确保了模型可识别性。我们提出一种两步估计方法：第一步利用外部信息估计边际病例比例；第二步使用该估计值构建加权目标函数用于参数训练。采用深度神经网络进行函数逼近，并推导出所提估计器的非渐近误差界。进一步获得收敛速率，证明其达到非参数回归估计的最优速度。通过模拟研究评估理论结果，一个真实数据例子用于说明方法应用。
原文摘要 · Abstract (English)
The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external summary information. The incorporation of external summary information ensures the identifiability of the model. We propose a two-step estimation procedure. In the first step, the external information is utilized to estimate the marginal case proportion. In the second step, the estimated proportion is used to construct a weighted objective function for parameter training. A deep neural network architecture is employed for functional approximation. We further derive the non-asymptotic error bound of the proposed estimator. Following this the convergence rate is obtained and is shown to reach the optimal speed of the non-parametric regression estimation. Simulation studies are conducted to evaluate the theoretical findings of the proposed method. A real data example is analyzed for illustration.
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