  Current methods of blended targets domain adaptation (BTDA) usually infer or
consider domain label information but underemphasize hybrid categorical feature
structures of targets, which yields limited performance, especially under the
label distribution shift. We demonstrate that domain labels are not directly
necessary for BTDA if categorical distributions of various domains are
sufficiently aligned even facing the imbalance of domains and the label
distribution shift of classes. However, we observe that the cluster assumption
in BTDA does not comprehensively hold. The hybrid categorical feature space
hinders the modeling of categorical distributions and the generation of
reliable pseudo labels for categorical alignment. To address these, we propose
a categorical domain discriminator guided by uncertainty to explicitly model
and directly align categorical distributions $P(Z|Y)$. Simultaneously, we
utilize the low-level features to augment the single source features with
diverse target styles to rectify the biased classifier $P(Y|Z)$ among diverse
targets. Such a mutual conditional alignment of $P(Z|Y)$ and $P(Y|Z)$ forms a
mutual reinforced mechanism. Our approach outperforms the state-of-the-art in
BTDA even compared with methods utilizing domain labels, especially under the
label distribution shift, and in single target DA on DomainNet. Source codes
are available at
\url{https://github.com/Pengchengpcx/Class-overwhelms-Mutual-Conditional-Blended-Target-Domain-Adaptation}.
