Computational Efficiency under Covariate Shift in Kernel Ridge Regression

Andrea Della Vecchia (EPFL - Switzerland) · Arnaud Mavakala Watusadisi (University of Genoa) · Ernesto De Vito (Università degli Studi di Genova) · Lorenzo Rosasco (Massachusetts Institute of Technology)

computational efficiency covariate shift hypothesis spaceinput distributionskernel methodslarge datasetslearning performancememory scalabilitynonparametric regressionrandom projectionsrandom subspacereproducing kernel hilbert spacesstatistical accuracystatistical properties supervised learning trade-off

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.