DivideandContrast: Source-freeDomainAdaptation viaAdaptiveContrastiveLearning (SupplementaryMaterial)

Consideringa C-wayclassification task, our model consists of source classifier and feature extractor h = gs ϕ, which maps input spaceRI topredictionvector spaceRC,andh(x) = argmaxc h(x)[c]. Following in[25,26,27,28],wedenoteDTc astheconditional distribution (probability measure) ofDT given the ground truthy = c, and also assume that the supports ofDTi andDTj aredisjointforalli = j. Following [25, 27, 26], we study target domain relies on theexpansion property, which implies the continuity of data distributions in each class-wise subpopulations. Thus, x DS,x B(x) DS, the network predictions are consistent, i.e.RDS(h)=0. Theorem A.2. Suppose the condition of Claim 3.1 holds andDT,DS satisfies (q,γ)-constant expansion.