A Unified View of Double-Weighting for Marginal Distribution Shift

Supervised classification traditionally assumes that training and testing samples are drawn from the same underlying distribution. However, practical scenarios are often affected by distribution shifts, such as covariate and label shifts. Most existing techniques for correcting distribution shifts are based on a reweighted approach that weights training samples, assigning lower relevance to the samples that are unlikely at testing. However, these methods may achieve poor performance when the weights obtained take large values at certain training samples. In addition, in multi-source cases, existing methods do not exploit complementary information among sources, and equally combine sources for all instances. In this paper, we establish a unified learning framework for distribution shift adaptation. We present a double-weighting approach to deal with distribution shifts, considering weight functions associated with both training and testing samples. For the multi-source case, the presented methods assign source-dependent weights for training and testing samples, where weights are obtained jointly using information from all sources. We also present generalization bounds for the proposed methods that show a significant increase in the effective sample size compared with existing approaches. Empirically, the proposed methods achieve enhanced classification performance in both synthetic and empirical experiments.