Open Set Domain Adaptation via Known Joint Distribution Matching and Unknown Classification Risk Reformulation

Open set domain adaptation (OSDA) is an important problem in machine learning and computer vision. In OSDA, one is given a labeled dataset from a source domain (source joint distribution) and an unlabeled dataset from a target domain (target joint distribution), where the target domain contains not only the known classes presented in the source domain but also the unknown class. The goal of OSDA is to train a neural network with minimal target classification risk. From the statistical learning perspective, there are two fundamental challenges in this problem: (1) the source-target joint distribution difference regarding the known classes and (2) the target classification risk estimation regarding the unknown class. Although prior works have proposed various sophisticated solutions to the problem and achieved inspiring experimental results, they do not fully resolve these two challenges. In this article, we introduce a principled approach named known joint distribution matching and unknown classification risk reformulation (KMUR). KMUR tackles the first challenge by matching the source joint distribution to the target known joint distribution such that the distribution difference can be reduced and addresses the second challenge by reformulating the target unknown classification risk such that the reformulated risk can be estimated on the unlabeled target and source data. To be specific, we exploit cross entropy as the classification loss and triangular discrimination (TD) distance as the joint distribution matching loss. Since the TD distance needs to be estimated from data, we develop an innovative technique named least squares TD estimation (LSTDE), which casts the estimation into least squares classification. To achieve the OSDA goal, we train the network to minimize the estimations of target classification risk and TD distance. Experiments on benchmark and real-world datasets confirm the effectiveness of our approach. The introductory video and PyTorch code are available on GitHub (https://github.com/sentaochen/Known-Joint-Distribution-Matching-and-Unknown-Classification-Risk-Reformulation). One can also visit https://github.com/sentaochen for more source code on domain adaptation (DA), multi-source DA, partial DA, and domain generalization approaches.