Class Prior Estimation under Covariate Shift: No Problem?
This addresses a fundamental limitation in domain adaptation for classification when covariate information is reduced, though the contribution appears incremental to existing covariate shift theory.
The paper demonstrates that covariate shift relationships between source and target distributions can be disrupted when reducing covariate information, making standard class prior estimation methods infeasible. It proves that only statistically sufficient transformations preserve covariate shift and proposes a probing algorithm as an alternative estimation approach.
We show that in the context of classification the property of source and target distributions to be related by covariate shift may be lost if the information content captured in the covariates is reduced, for instance by dropping components or mapping into a lower-dimensional or finite space. As a consequence, under covariate shift simple approaches to class prior estimation in the style of classify and count with or without adjustment are infeasible. We prove that transformations of the covariates that preserve the covariate shift property are necessarily sufficient in the statistical sense for the full set of covariates. A probing algorithm as alternative approach to class prior estimation under covariate shift is proposed.