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 mostly 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 to label distribution estimation 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）是一种包含协变量偏移和标签偏移的分布偏移（或数据集偏移）。近期研究发现，FJS实际上是由连续的标签偏移和协变量偏移（或反之）产生的。迄今为止，对FJS的研究主要局限于分类标签的情形。我们提出一个框架用于分析一般标签空间下的分布偏移，从而同时涵盖分类模型和回归模型。基于该框架，我们将FJS的现有结果推广至一般标签空间，并提出并分析一种关于标签分布估计的期望最大化（EM）算法在类别先验概率上的相关扩展。此外，我们从全新视角审视了一般标签空间下的广义标签偏移（GLS）。