研究了在函数不满足光滑性假设时，核方法的采样收敛性。
Convergence Analysis of Nyström Subsampling in Covariate Shift Adaptation for Misspecified case
- 用正则化+子采样投影分析低光滑情况下的误差上界。
- 给出了在源数据分布未知时仍保持收敛速度所需的最小样本量。
- 适合关注鲁棒迁移学习与核方法理论的研究者阅读。
本文研究在协变量偏移下，针对函数不满足光滑性假设（即目标函数不在再生核希尔伯特空间内）的无监督域适应问题中，正则化Nyström子采样的收敛性质。通过结合Tikhonov正则化与在子采样子空间上的Nyström投影，我们获得了在高概率下成立的过失风险上界，其形式依赖于源条件、有效维度和样本量。进一步地，分析扩展到目标与源分布之间的Radon-Nikodym导数未知的情形，需通过近似估计，我们识别出维持与已知情形相同收敛速率所需的最小额外样本量。
原文摘要 · Abstract (English)
This paper investigates convergence properties of regularized Nyström subsampling applied to the unsupervised domain adaptation problem under covariate shift. We focus on the low-smoothness (misspecified) case where the target function lies outside the reproducing kernel Hilbert space. By combining Tikhonov regularization with Nyström projection onto a subsampled subspace, we obtain upper bounds on the excess risk that hold with high probability and are expressed in terms of the source condition, the effective dimension, and the sample sizes. We further extend the analysis to the setting where the Radon-Nikodym derivative between the target and source marginal distributions is unknown and must be approximated, and we identify the minimal additional sample sizes required to maintain the same convergence rate as in the oracle case.
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