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Machine learning systems may encounter unexpected problems when the datadistribution changes in the deployment environment. A major reason is thatcertain combinations of domains and labels are not observed during training butappear in the test environment. Although various invariance-based algorithmscan be applied, we find that the performance gain is often marginal. Toformally analyze this issue, we provide a unique algebraic formulation of thecombination shift problem based on the concepts of homomorphism, equivariance,and a refined definition of disentanglement. The algebraic requirementsnaturally derive a simple yet effective method, referred to as equivariantdisentangled transformation (EDT), which augments the data based on thealgebraic structures of labels and makes the transformation satisfy theequivariance and disentanglement requirements. Experimental results demonstratethat invariance may be insufficient, and it is important to exploit theequivariance structure in the combination shift problem.

Equivariant Disentangled Transformation for Domain Generalization under Combination Shift