Computational Efficiency under Covariate Shift in Kernel Ridge Regression

TL;DR

This paper explores how to reduce computational costs in kernel ridge regression under covariate shift by using random projections, achieving efficiency gains while maintaining accuracy.

Contribution

It introduces a method using random subspaces within RKHS to balance computational efficiency and statistical accuracy under covariate shift.

Findings

Significant computational savings are possible with minimal loss in accuracy.

Random projections effectively handle covariate shift in kernel methods.

The approach scales better to large datasets without sacrificing performance.

Abstract

This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and test data differ, presenting additional challenges for learning. Although kernel methods have optimal statistical properties, their high computational demands in terms of time and, particularly, memory, limit their scalability to large datasets. To address this limitation, the main focus of this paper is to explore the trade-off between computational efficiency and statistical accuracy under covariate shift. We investigate the use of random projections where the hypothesis space consists of a random subspace within a given RKHS. Our results show that, even in the presence of covariate shift, significant computational savings can be achieved without compromising learning performance.