The ability of a classifier to recognize unknown inputs is important for many classification-based systems. We discuss the problem of simultaneous classification and novelty detection, i.e. determining whether an input is from the known set of classes and from which specific class, or from an unknown domain and does not belong to any of the known classes. We propose a method based on the Generative Adversarial Networks (GAN) framework. We show that a multi-class discriminator trained with a generator that generates samples from a mixture of nominal and novel data distributions is the optimal novelty detector. We approximate that generator with a mixture generator trained with the Feature Matching loss and empirically show that the proposed method outperforms conventional methods for novelty detection. Our findings demonstrate a simple, yet powerful new application of the GAN framework for the task of novelty detection.
This paper proposed a GAN to unify classification and novelty detection. The technical difficulty is acceptable, but there are several issues. First of all, the motivation is clearly given in the 1st paragraph of the introduction: "In fact for such novel input the algorithm will produce erroneous output and classify it as one of the classes that were available to it during training. Ideally, we would like that the classifier, in addition to its generalization ability, be able to detect novel inputs, or in other words, we would like the classifier to say, 'I don't know.'" There is a logical gap between the ability of saying 'I don't know' and the necessity of novelty detection. Moreover, there are many papers known as "learning with abstention" and/or "learning with rejection" from NIPS, ICML, COLT, etc. (some are coauthored by Dr. Peter Bartlett or Dr. Corinna Cortes), but the current paper didn't cite those that are particularly designed to let the classifier be able to say 'I don't know'. All those abstention/rejection papers have solid theoretical guarantees.
The 3rd issue is that the novelty for the novelty detection part in the proposed GAN seems quite incremental. As mentioned in the paper, there are already a few GANs, such that "If the 'real' data consists of K classes, then the output of the discriminator is K+1 class probabilities where K probabilities corresponds to K known classes, and the K+1 probability correspond to the 'fake' class." On the other hand, the idea in this paper is that "At test time, when the discriminator classifies a real example to the K+1th class, i.e., class which represented 'fake examples' during training, this the example is most likely a novel example and not from one of the K nominal classes." This is just a replacement of concepts, where the original one is the fake class in training and the new one is the novel class in test. Furthermore, the 4th issue also comes from this replacement. The proposed method assumes a very strong distributional assumption, that is, the class-conditional density of the union of all novel classes at test time is very similar to the class-conditional density of the fake class at training time, where the choice of similarity depends on the divergence measure for training GAN. This assumption is too strong for the application of novelty detection, since novel data can be whatsoever unseen during training.
This inconsistency leads to the last issue. Again mentioned in the 1st paragraph, "there are no requirements whatsoever on how the
classifier should behave for new types of input that differ substantially from the data that are available during training". This evidences that novel data can be whatsoever unseen during training (per my words). However, the ultimate goal of the generator is to fool the discriminator by generating fake data as similar to the real data as possible in all types of GANs. Therefore, it is conceptually and theoretically strange to apply GAN to novelty detection, which is the major contribution of this paper.
Last but not least, there is an issue not quite directly related to this paper. Novelty detection sounds very data mining rather than machine learning. It is fully unsupervised without a clearly-defined goal which makes it sounds like an art rather than a science. The experimental performance is promising indeed, but a lot of domain knowledge is involved in the experiment design. I am not sure they are really novelty detection tasks because the real novelty detection tasks should be fully exploratory. 
BTW, there is a paper in IPMI 2017 entitled "Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery", which is very closely related to the current paper but the authors seem not aware of it.