Computational Efficiency under Covariate Shift in Kernel Ridge Regression
This addresses scalability issues for kernel methods in supervised learning when training and test data distributions differ, but it is incremental as it builds on existing random projection techniques.
The paper tackles the computational inefficiency of kernel methods under covariate shift by using random projections in RKHS, achieving significant computational savings without compromising learning performance.
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.