Factorizable joint shift was recently proposed as a type of dataset shift for which the characteristics can be estimated from observed data. For the multinomial (multi-class) classification setting, we derive a representation of factorizable joint shift in terms of the source (training) distribution, the target (test) prior class probabilities and the target marginal distribution of the features. On the basis of this result, we propose alternatives to joint importance aligning, at the same time pointing out the limitations encountered when making an assumption of factorizable joint shift. Other results of the paper include correction formulae for the posterior class probabilities both under general dataset shift and factorizable joint shift. In addition, we investigate the consequences of assuming factorizable joint shift for the bias caused by sample selection.

中文翻译：

---

多项分类中的可分解联合移位

最近提出了可分解的联合移位作为一种数据集移位，可以从观察到的数据中估计其特征。对于多项（多类）分类设置，我们根据源（训练）分布、目标（测试）先验类概率和特征的目标边际分布推导出可分解联合移位的表示。在此结果的基础上，我们提出了联合重要性对齐的替代方案，同时指出了在假设可分解联合偏移时遇到的限制。本文的其他结果包括在一般数据集移位和可分解联合移位下的后验类概率的校正公式。此外，