Bridging the Theoretical Bound and Deep Algorithms for Open Set Domain Adaptation

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 $ ), distributional discrepancy between domains, and a constant. Compared with 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 with the existing shallow and deep UOSDA methods, our method shows the state-of-the-art performance on several benchmark datasets, including digit recognition [modified National Institute of Standards and Technology database (MNIST), the Street View House Number (SVHN), U.S. Postal Service (USPS)], object recognition (Office-31, Office-Home), and face recognition [pose, illumination, and expression (PIE)].