  In the unsupervised open set domain adaptation (UOSDA), the target domain
contains unknown classes that are not observed in the source domain.
Researchers in this area aim to train a classifier to accurately: 1) recognize
unknown target data (data with unknown classes) and, 2) classify other target
data. To achieve this aim, a previous study has proven an upper bound of the
target-domain risk, and the open set difference, as an important term in the
upper bound, is used to measure the risk on unknown target data. By minimizing
the upper bound, a shallow classifier can be trained to achieve the aim.
However, if the classifier is very flexible (e.g., deep neural networks
(DNNs)), the open set difference will converge to a negative value when
minimizing the upper bound, which causes an issue where most target data are
recognized as unknown data. To address this issue, we propose a new upper bound
of target-domain risk for UOSDA, which includes four terms: source-domain risk,
$\epsilon$-open set difference ($\Delta_\epsilon$), a distributional
discrepancy between domains, and a constant. Compared to the open set
difference, $\Delta_\epsilon$ is more robust against the issue when it is being
minimized, and thus we are able to use very flexible classifiers (i.e., DNNs).
Then, we propose a new principle-guided deep UOSDA method that trains DNNs via
minimizing the new upper bound. Specifically, source-domain risk and
$\Delta_\epsilon$ are minimized by gradient descent, and the distributional
discrepancy is minimized via a novel open-set conditional adversarial training
strategy. Finally, compared to existing shallow and deep UOSDA methods, our
method shows the state-of-the-art performance on several benchmark datasets,
including digit recognition (MNIST, SVHN, USPS), object recognition (Office-31,
Office-Home), and face recognition (PIE).
