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We study the minimax rates of the label shift problem in non-parametricclassification. In addition to the unsupervised setting in which the learneronly has access to unlabeled examples from the target domain, we also considerthe setting in which a small number of labeled examples from the target domainis available to the learner. Our study reveals a difference in the difficultyof the label shift problem in the two settings, and we attribute thisdifference to the availability of data from the target domain to estimate theclass conditional distributions in the latter setting. We also show that aclass proportion estimation approach is minimax rate-optimal in theunsupervised setting.

Minimax optimal approaches to the label shift problem in non-parametric settings