Hanna Myleiko | Searcharxiv

arXiv2026

Convergence Analysis of Nystr\"om Subsampling in Covariate Shift Adaptation for Misspecified case

This paper investigates convergence properties of regularized Nystr\"om 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 Nystr\"om 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.

stat.ML↗

arXiv2025

On recovering the Radon-Nikodym derivative under the big data assumption

The present paper is focused on the problem of recovering the Radon-Nikodym derivative under the big data assumption. To address the above problem, we design an algorithm that is a combination of the Nystr\"om subsampling and the standard Tikhonov regularization. The convergence rate of the corresponding algorithm is established both in the case when the Radon-Nikodym derivative belongs to RKHS and in the case when it does not. We prove that the proposed approach not only ensures the order of accuracy as algorithms based on the whole sample size, but also allows to achieve subquadratic computational costs in the number of observations.

math.NA↗