A new similarity measure for covariate shift with applications to nonparametric regression

2022/02/06 by Pathak, Reese, Ma, Cong, Wainwright, Martin J. · 3 citations
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2202.02837

Abstract

We study covariate shift in the context of nonparametric regression. We introduce a new measure of distribution mismatch between the source and target distributions that is based on the integrated ratio of probabilities of balls at a given radius. We use the scaling of this measure with respect to the radius to characterize the minimax rate of estimation over a family of Hölder continuous functions under covariate shift. In comparison to the recently proposed notion of transfer exponent, this measure leads to a sharper rate of convergence and is more fine-grained. We accompany our theory with concrete instances of covariate shift that illustrate this sharp difference.

Cited by

• On a synergistic learning phenomenon in nonparametric domain adaptation
• A Conditional Distribution Equality Testing Framework using Deep Generative Learning
• Vector preference-based contextual bandits under distributional shifts

Related

• Transfer Learning under Covariate Shift: Local k-Nearest Neighbours Regression with Heavy-Tailed Design
• Nearest Neighbor Sampling for Covariate Shift Adaptation
• Covariate Shift in High-Dimensional Random Feature Regression
• Optimally tackling covariate shift in RKHS-based nonparametric regression
• Phase Transition in Nonparametric Minimax Rates for Covariate Shifts on Approximate Manifolds