发表机构
University of California, Los Angeles; Washington University in St. Louis; Hong Kong University of Science and Technology（加利福尼亚大学洛杉矶分校; 圣路易斯华盛顿大学; 香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对多组数据的非参数回归，提出基于深度ReLU网络的两阶段偏移学习迁移框架，通过理论分析与实验验证，证明其可克服维度诅咒并实现有效迁移。
AI 中文摘要
本文针对由多组数据构成的非参数回归问题，提出了一种通用迁移学习框架。在各组数据共享共同结构且存在加性形式的组特定偏差的假设下，所提方法采用两阶段偏移学习流程：第一阶段汇集所有组的数据以估计整体均值函数，第二阶段估计每组的偏移量，通过加性组合得到最终的组级估计量。针对该框架建立了$\boldsymbol{\textit{L}}_2$误差的上界，在温和的复杂度与噪声条件下，覆盖了广泛类别的非参数估计量。当以深度ReLU网络作为实例时，在分层组合模型下推导了显式收敛速率，证明其具备克服维度诅咒的能力。本文还考虑了能实现更快速率正迁移的条件，包括使用更简单函数学习以及跨组合并样本的数据增强。大量模拟与真实数据实验进一步验证了所提方法的有效性。
英文摘要
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.
CommentsAccepted at the 43rd International Conference on Machine Learning (ICML 2026)
