We consider a semi-supervised classification problem with non-stationary
label-shift in which we observe a labelled data set followed by a sequence of
unlabelled covariate vectors in which the marginal probabilities of the class
labels may change over time. Our objective is to predict the corresponding
class-label for each covariate vector, without ever observing the ground-truth
labels, beyond the initial labelled data set. Previous work has demonstrated
the potential of sophisticated variants of online gradient descent to perform
competitively with the optimal dynamic strategy (Bai et al. 2022). In this work
we explore an alternative approach grounded in statistical methods for adaptive
transfer learning. We demonstrate the merits of this alternative methodology by
establishing a high-probability regret bound on the test error at any given
individual test-time, which adapt automatically to the unknown dynamics of the
marginal label probabilities. Further more, we give bounds on the average
dynamic regret which match the average guarantees of the online learning
perspective for any given time interval.

我们研究了一个具有非平稳标签转移的半监督分类问题，通过观察一组有标签的数据集和一系列无标签的协变量向量，我们的目标是预测每个协变量向量的相应类别标签，而无需观察除初始有标签数据集之外的真实标签。通过建立一个在任何给定测试时间内自适应地适应未知动态边缘标签概率的高概率遗憾上界，我们探索了一种基于统计方法的自适应迁移学习的替代方法，并给出了与在线学习方法相匹配的平均动态遗憾界限的界限。