Sparse joint shift (SJS) was recently proposed as a tractable model for general dataset shift which may cause changes to the marginal distributions of features and labels as well as the posterior probabilities and the class-conditional feature distributions. Fitting SJS for a target dataset without label observations may produce valid predictions of labels and estimates of class prior probabilities. We present new results on the transmission of SJS from sets of features to larger sets of features, a conditional correction formula for the class posterior probabilities under the target distribution, identifiability of SJS, and the relationship between SJS and covariate shift. In addition, we point out inconsistencies in the algorithms which were proposed for estimating the characteristics of SJS, as they could hamper the search for optimal solutions.

翻译：最近，稀疏联合移位 (SJS) 被提出作为一种适用于数据集移位，它可能会导致特征和标签的边缘分布以及后验概率和类条件特征分布的变化的可行模型。在没有标签观测的情况下为目标数据集拟合 SJS 可能会产生有效的标签预测和类先验概率估计。我们在特征集合和更大特征集合之间传输 SJS、给出了目标分布下类后验概率的条件修正公式、SJS 的可辨别性以及 SJS 和协变量移位之间的关系等新的结果。另外，我们指出了针对估计 SJS 特征的算法的不一致性，因为它们可能会妨碍寻找最优解。