Computational Efficiency under Covariate Shift in Kernel Ridge Regression

2025-05-20

AI Summary

This paper addresses the scalability bottleneck of kernel ridge regression (KRR) under covariate shift for large-scale datasets. We propose an efficient algorithm based on random subspace projection in a reproducing kernel Hilbert space (RKHS). Our key contribution is the first theoretical guarantee—under covariate shift—that random projection achieves near-optimal statistical error rate $O(n^{-1/2})$ while reducing time and memory complexity from $O(n^3)$ and $O(n^2)$ to $O(mn)$ and $O(m)$, respectively, where $m ll n$. Crucially, the method avoids explicit estimation of covariate shift weights, ensuring both theoretical rigor and practical deployability. Empirical results demonstrate significant speedups (several-fold acceleration) and substantial memory reduction, without sacrificing predictive accuracy.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Addressing covariate shift in RKHS nonparametric regression
• Balancing computational efficiency and statistical accuracy
• Using random projections for scalable kernel methods

Innovation

• Uses random projections in RKHS
• Balances computational efficiency and accuracy
• Reduces memory and time demands