超越源级迁移：高维分位数回归的样本级学习
Beyond Source-Level Transfer: Sample-Level Learning for High-Dimensional Quantile Regression
- Renmin University of China（中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对高维分位数回归的迁移学习，提出样本级迁移方法 SL-TL，通过样本选择与重要性加权利用源域可迁移样本，实现更快的收敛速率并展现稳健性能。
中文摘要 AI 辅助
本文研究了在目标样本有限且源域异质的情况下，高维分位数回归的迁移学习问题。我们提出了一种样本级迁移学习方法（SL-TL），该方法结合了样本选择与重要性加权。与现有的源级方法（即包含或排除整个源域）不同，SL-TL 在每个源域内识别可迁移的样本，并通过自适应重要性权重将其纳入。所提出的权重仅依赖于与分位数损失相关的一维密度，从而避免了高维密度比的估计。我们为 SL-TL 估计量建立了误差界，并刻画了源域所贡献的有效样本量。在理想（oracle）设定下，我们证明 SL-TL 在所考虑的机制下比现有竞争者实现了更快的 $\ell_2$ 收敛速率。对于未知设定，我们开发了一种基于样本分割和交叉拟合过程的可实现算法。广泛的模拟实验和一项真实数据分析展示了 SL-TL 的有限样本性能和稳健性。
英文摘要
This paper studies transfer learning for high-dimensional quantile regression with limited target samples and heterogeneous source domains. We propose a sample-level transfer learning method (SL-TL) that combines sample selection and importance weighting. Unlike existing source-level approaches that include or exclude entire source domains, SL-TL identifies transferable samples within each source domain and incorporates them through adaptive importance weights. The proposed weights rely only on one-dimensional densities associated with the quantile loss, avoiding the estimation of high-dimensional density ratios. We establish error bounds for SL-TL estimators and characterize the effective sample size contributed by source domains. In the oracle setting, we show that SL-TL achieves faster $\ell_2$-convergence rates than existing competitors under the considered regimes. For the unknown setting, we develop an implementable algorithm based on sample splitting and cross-fitting procedures. Extensive simulations and a real data analysis demonstrate the finite-sample performance and robustness of SL-TL.
