Factorizable joint shift (FJS) represents a type of distribution shift (or dataset shift) that comprises both covariate and label shift. Recently, it has been observed that FJS actually arises from consecutive label and covariate (or vice versa) shifts. Research into FJS so far has been confined to the case of categorical labels. We propose a framework for analysing distribution shift in the case of a general label space, thus covering both classification and regression models. Based on the framework, we generalise existing results on FJS to general label spaces and present and analyse a related extension of the expectation maximisation (EM) algorithm for class prior probabilities. We also take a fresh look at generalized label shift (GLS) in the case of a general label space.

翻译：可分解联合偏移（FJS）是一种同时包含协变量偏移和标签偏移的分布偏移（或数据集偏移）。最近研究表明，FJS实际上源于连续的标签偏移与协变量偏移（或反之）。目前对FJS的研究仅限于分类标签情形。本文提出一个适用于通用标签空间的分布偏移分析框架，从而同时涵盖分类与回归模型。基于该框架，我们将现有FJS研究成果推广至通用标签空间，提出并分析了类别先验概率期望最大化（EM）算法的相关扩展。此外，我们重新审视了通用标签空间下的广义标签偏移（GLS）问题。