用深度网络做多组非参数回归，共享结构+分组偏差，提升预测精度。
Transfer Learning in Nonparametric Regression with Deep ReLU Networks
- 先合起来学整体趋势，再学每组差异，最后加起来得结果。
- 在高维数据下，用深层ReLU网络仍能快速收敛，突破维度瓶颈。
- 适合有多个相似但不完全相同的子数据集的场景，如跨领域建模。
本文为多组非参数回归提出一个通用迁移学习框架。假设各组共享共同结构并带有加性形式的组间偏差，方法采用两阶段偏移学习：第一阶段合并所有组数据估计全局均值函数；第二阶段估计各组偏移量，通过加法组合得到最终组级估计器。在温和复杂度与噪声条件下，建立了所提框架的$/mathcal L_2$误差上界，涵盖广泛非参数估计器。当使用深层ReLU网络实现时，在层级组合模型下导出明确收敛速率，证明可克服维度灾难。研究了实现正迁移（更快收敛）的条件，包括学习简单函数及跨组样本池化带来的数据增强。多种模拟实验与真实数据验证了方法的有效性。
原文摘要 · Abstract (English)
This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data from all groups to estimate an overall mean function, and the second stage estimates offsets for each group, yielding final group-level estimators through additive combination. Upper bounds on the $\mathcal L_2$ error are established for the proposed framework, covering a broad class of nonparametric estimators under mild complexity and noise conditions. When instantiated with deep ReLU networks, explicit convergence rates are derived under hierarchical composition models, demonstrating the ability to overcome the curse of dimensionality. Conditions that enable positive transfer with faster rates are considered, including learning with simpler functions and data augmentation through pooling samples across groups. Various simulations and real-data experiments further validate the effectiveness of the proposed method.
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