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In massive data analysis, training and testing data often come from verydifferent sources, and their probability distributions are not necessarilyidentical. A feature example is nonparametric classification in posterior driftmodel where the conditional distributions of the label given the covariates arepossibly different. In this paper, we derive minimax rate of the excess riskfor nonparametric classification in posterior drift model in the setting thatboth training and testing data have smooth distributions, extending a recentwork by Cai and Wei (2019) who only impose smoothness condition on thedistribution of testing data. The minimax rate demonstrates a phase transitioncharacterized by the mutual relationship between the smoothness orders of thetraining and testing data distributions. We also propose a computationallyefficient and data-driven nearest neighbor classifier which achieves theminimax excess risk (up to a logarithm factor). Simulation studies and areal-world application are conducted to demonstrate our approach.

A Computationally Efficient Classification Algorithm in Posterior Drift Model: Phase Transition and Minimax Adaptivity