Paper:
Positive Unlabeled (PU) learning consists in learning to distinguish samples of our class of interest, the positive class, from the counter-examples, the negative class, by using positive labeled and unlabeled samples during the training. Recent approaches exploit the GANs abilities to address the PU learning problem by generating relevant counter-examples. In this paper, we propose a new GAN-based PU learning approach named Divergent-GAN (D-GAN). The key idea is to incorporate a standard Positive Unlabeled learning risk inside the GAN discriminator loss function. In this way, the discriminator asks the generator to converge towards the unlabeled samples distribution while diverging from the positive samples distribution. This enables the generator convergence towards the unlabeled counterexamples distribution without using prior knowledge, while keeping the standard adversarial GAN architecture. In addition, we discuss normalization techniques in the context of the proposed framework. Experimental results show that the proposed approach overcomes previous GAN-based PU learning methods issues, and it globally outperforms two-stage state of the art PU learning performances in terms of stability and prediction on both simple and complex image datasets.

Review:
This paper proposed another GAN-based PU learning method. The mathematics in this paper is not easy to follow, and there are many other critical issues.
*****
The clarity is really an issue. First of all, I cannot easily follow the meanings behind the equations. I guess the authors first came up with some concrete implementation and then formalize it into an algorithm. Given the current version of the paper, I am not sure whether this clarity of equations can be fixed without an additional round of review or not.
Moreover, the logic in the story line is unclear to me, especially the 3rd paragraph that seems to be mostly important in the introduction. There are two different binary classification problems, of separating the positive and negative classes, and of separating the given and generated data. I cannot see why the generated data can serve as negative data. This paragraph is discussing GenPU, PGAN and the proposed method, and consequently the motivation of the current paper does not make sense at least to me.
*****
The paper classified PU learning methods into two categories, one-stage methods and two-stage methods. This is interesting. However, before that, they should be classified into two categories, for censoring PU learning and for case-control PU learning. The former problem setting was proposed very early and formalized in "learning classifiers from only positive and unlabeled data", KDD 2008; the latter problem setting was proposed in "presence-only data and the EM algorithm", Biometrics 2009 and formalized in "analysis of learning from positive and unlabeled data", NIPS 2014. Surprisingly, none of these 3 papers was cited. By definition, GAN-based PU learning belongs to the latter problem setting while Rank Prune can only be applied to the former but was included as a baseline method.
The huge difference between these two settings and their connections to learning with noisy labels are known for long time. To be short, class-conditional noise model corrupts P(Y|X) and covers censoring PU, mutual contamination distribution framework corrupts P(X|Y) and covers case-control PU, and mathematically mutual contamination distribution framework is more general than class-conditional noise model and so is case-control PU than censoring PU. See "learning from corrupted binary labels via class-probability estimation", ICML 2015 for more information where the above theoretical result has been proven. An arXiv paper entitled "on the minimal supervision for training any binary classifier from only unlabeled data" has some experimental results showing that methods for class-conditional noise model cannot handle mutual contamination distributions. The situation is similar when applying censoring PU methods to case-control PU problem setting.
Furthermore, the class-prior probability pi is well-defined and easy to estimate in censoring PU, see "learning classifiers from only positive and unlabeled data" mentioned above. However, it is not well-defined in case-control PU due to an identifiability issue described in "presence-only data and the EM algorithm" mentioned above. Thus, the target to be estimated is defined as the maximal theta such that theta*P(X|Y)<=P(X) following "estimating the class prior and posterior from noisy positives and unlabeled data", NIPS 2016. BTW, "mixture proportion estimation via kernel embedding of distributions" is SOTA in class-prior estimation; the previous NIPS paper was written earlier and accepted later.
In summary, as claimed in the paper and shown in Table 1 in the introduction, all discriminative PU methods and GenPU require to know pi for learning. This is true, but this is because they are designed for a more difficult problem setting---learning classifiers and estimating pi are both more difficult. Lacking some basic knowledge of PU learning is another big issue.
*****
The novelty is to be honest incremental and thus below the bar of ICLR. The significance is similarly poor, due to that the experiments mixed up methods for censoring PU and those for case-control PU. What is more, F1-score is a performance measure for information retrieval rather than binary classification. We all know GANs are pretty good at MNIST but not CIFAR-10. In fact, GenPU has a critical issue of mode collapse, and this is why GenPU reports 1-vs-1 rather than 5-vs-5 on MNIST. Even though, I still think GenPU makes much more sense than PGAN and D-GAN.