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

arXiv: https://arxiv.org/abs/2606.22259 · HTML: https://mlsanity.com/paper/2606.22259/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 20 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [When is Importance Weighting Correction Needed for Covariate Shift Adaptation?](https://mlsanity.com/paper/2303.04020/) (2023)
- [On regularized Radon-Nikodym differentiation](https://mlsanity.com/paper/2308.07887/) (2023)
- [Computational Efficiency under Covariate Shift in Kernel Ridge Regression](https://mlsanity.com/paper/2505.14083/) (2025)
- [Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shift](https://mlsanity.com/paper/2509.05106/) (2025)

## Abstract (arXiv)

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.