# Extending Partial Domain Adaptation Algorithms to the Open-Set Setting
## 1 Introduction  
Supervised learning techniques work under the assumption that training and testing datasets are drawn from the same distribution. Thus, traditional techniques require at least some labeled data for the problem at hand so as to obtain a useful model upon training, which, in many cases, is not possible. Domain adaptation (DA) [1] is a technique for generalizing classifiers to different domains. More specifically, given two datasets with the same label space, with one of them labeled (the _source_), a DA algorithm may retrieve labels for the other (the _target_). Note that this does not make any assumption on the underlying distributions of data, yet it is still quite restrictive, since it requires the two datasets to have the same labels.  
In practice, we are typically interested in extracting labels from datasets with much larger label spaces than any specific task dataset [2]. To this end, the partial domain adaptation (PDA) [2, 3] framework was proposed, in which the assumption is that labels for target data are contained within the larger label space of source data. Of course, the creation of such general-purpose source datasets, which represent the entire label space of any given specific task well, is unrealistic. As an example, some of the largest image datasets currently available [4, 5] are comprised of millions of images, but many classes are under-represented.  
To address this issue, open-set domain adaptation (OSDA) was proposed [6], essentially combining open-set recognition (OSR) [7] and DA. The aim in OSDA is to automatically extract the information from the source relevant to the target and to identify target instances relevant to the source. That is, a non-empty intersection between the target and source label spaces is assumed, and the goal is to identify source and target instances with labels in the common label subspace. The advantage of identifying such instances is two-fold: It allows us to minimize negative transfer (i.e., the inclusion of source-specific features in the adapted representation) and to identify the subset of target instances that can be reliably labeled through the source.  
Note that we cannot hope to predict the label of a target instance belonging to a class not represented in the source label space; however, the advantage of identifying which instances belong to such classes is two-fold. Firstly, it allows us to minimize negative transfer (i.e., the inclusion of source-specific features in the adapted representation) during the adaptation procedure. Secondly, it allows us to identify the subset of target instances that can be reliably labeled using this source.  
In this paper, we propose an algorithm for tackling OSDA, which we term the =_Doubly Importance Weighted Adversarial Network_ (DIWAN), which was inspired by the distribution reweighing techniques introduced in [8]. Our algorithm bridges the gap between the adversarial neural network (ANN) techniques used in PDA and OSDA by taking into account outlier target instances during adaptation. We prove that our algorithm constructs a representation in the which source and target distributions of transfer-relevant instances (TRI) are aligned. Moreover, we empirically demonstrate that in the open-set setting, DIWAN outperforms non-adapted versions of the DA and PDA algorithms.  
The rest of this paper is organized as follows: In Section 2, we present related work and the contribution of DIWAN. Then, in Section 3, we provide the theoretical background and the methodology used by DIWAN. Moreover, the theoretical support for this work is presented in Section 4. An experimental evaluation of DIWAN is presented and discussed in Section 5, and conclusions are drawn in Section 7.