Changes in the data distribution at test time can have deleterious effects on the performance of predictive models $p(y|x)$.We consider situations where there are additional meta-data labels (such as group labels), denoted by $z$, that can account for such changes in the distribution.In particular, we assume that the prior distribution $p(y,z)$, which models the dependence between the class label $y$ and the nuisance factors $z$, may change across domains, either due to a change in the correlation between these terms, or a change in one of their marginals.However, we assume that the generative model for features $p(x|y,z)$ is invariant across domains.We note that this corresponds to an expanded version of the widely used label shift assumption, where the labels now also include the nuisance factors $z$.

Changes in the data distribution at test time can have deleterious effects on the performance of predictive models p(y x) .We consider situations where there are additional meta-data labels (such as group labels), denoted by z, that can account for such changes in the distribution.In particular, we assume that the prior distribution p(y,z), which models the dependence between the class label y and the "nuisance" factors z, may change across domains, either due to a change in the correlation between these terms, or a change in one of their marginals.However, we assume that the generative model for features p(x y,z) is invariant across domains.We note that this corresponds to an expanded version of the widely used "label shift" assumption, where the labels now also include the nuisance factors z .