  In unsupervised domain adaptation (UDA), classifiers for the target domain
(TD) are trained with clean labeled data from the source domain (SD) and
unlabeled data from TD. However, in the wild, it is difficult to acquire a
large amount of perfectly clean labeled data in SD given limited budget. Hence,
we consider a new, more realistic and more challenging problem setting, where
classifiers have to be trained with noisy labeled data from SD and unlabeled
data from TD -- we name it wildly UDA (WUDA). We show that WUDA ruins all UDA
methods if taking no care of label noise in SD, and to this end, we propose a
Butterfly framework, a powerful and efficient solution to WUDA. Butterfly
maintains four deep networks simultaneously, where two take care of all
adaptations (i.e., noisy-to-clean, labeled-to-unlabeled, and
SD-to-TD-distributional) and then the other two can focus on classification in
TD. As a consequence, Butterfly possesses all the conceptually necessary
components for solving WUDA. Experiments demonstrate that, under WUDA,
Butterfly significantly outperforms existing baseline methods.
