重复测量的广义深度回归
Generalized Deep Regression for Repeated Measurements
- Bristol Myers Squibb（百时美施贵宝）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出用ReLU深度神经网络估计重复测量数据的边际回归函数，通过凸损失和Oracle不等式，达到最优收敛速率，并支持点估计与推断。
AI中文摘要：
本文研究了使用ReLU深度神经网络，从具有重复二元、计数或连续响应的独立单元中估计边际回归函数的问题。在该模型中，我们假设每个单元内的依赖性由一个未观测的随机均值函数产生。然后，我们拟合一个具有凸广义回归损失的神经网络。我们通过将条件测量变异与单元间变异分离，展示了一个Oracle不等式。此外，我们证明了在$n$个单元和每个单元$m$次测量的情况下，ReLU网络在$\beta$-Hölder类上，可以达到积分均方误差的阶为$n^{-1}+(nm)^{-2\beta/(2\beta+d)}$（忽略对数因子）。我们还推导了针对不等簇大小的加权Oracle不等式，以及针对组合光滑函数的速率。对于逐点集成推断，我们给出了投影中心极限定理，并在显式渐近线性条件下证明了无穷小刀切法的一致性。我们提供了模拟和真实数据示例，以支持我们的理论发现和实际意义。
英文摘要：
In this paper, we study the estimation of a marginal regression function from independent units with repeated binary, count, or continuous responses using ReLU deep neural networks. In the model, we assume that the dependence is generated by an unobserved random mean function within each unit. We then fit a neural network with a convex generalized regression loss. We show an oracle inequality by separating conditional measurement variation from between-unit variation. In addition, we prove that with $n$ units and $m$ measurements per unit, ReLU networks can attain an integrated mean squared error of order $n^{-1}+(nm)^{-2β/(2β+d)}$, up to logarithmic factors, over $β$-Hölder classes. We also derive a weighted oracle inequality for unequal cluster sizes and a rate for compositionally smooth functions. For pointwise ensemble inference, we give a projection central limit theorem and prove infinitesimal jackknife consistency under an explicit asymptotic linearity condition. Simulations and real data examples are provided to support our theoretical findings and practical implications.
