As an important semi-supervised learning task, positive-unlabeled (PU) learning aims to learn a binary classifier only from positive and unlabeled data. In this article, we develop a novel PU learning framework, called discriminative adversarial networks, which contains two discriminative models represented by deep neural networks. One model @math predicts the conditional probability of the positive label for a given sample, which defines a Bayes classifier after training, and the other model @math distinguishes labeled positive data from those identified by @math . The two models are simultaneously trained in an adversarial way like generative adversarial networks, and the equilibrium can be achieved when the output of @math is close to the exact posterior probability of the positive class. In contrast with existing deep PU learning approaches, DAN does not require the class prior estimation, and its consistency can be proved under very general conditions. Numerical experiments demonstrate the effectiveness of the proposed framework.
It is also interesting to compare DAN to GenPU, a GAN based PU learning method @cite_23 , since they share the similar adversarial training architecture. In DAN, the discriminative model @math plays the role of the generative model in GAN by approximating positive data distribution in an implicit way, and can be efficiently trained together with @math . In contrast, GenPU is much more time-consuming and easily suffers from mode collapse as stated in @cite_23 due to that it contains three generators and two discriminators. (Notice that the penalty factor @math cannot be applied to GenPU for the probability densities of samples given by generators are unknown.) Furthermore, the consistency of the GenPU needs the assumptions that class prior is given and there is no overlapping between positive and negative data distributions, which are not necessary for DAN.
@cite_23
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In this work, we consider the task of classifying binary positive-unlabeled (PU) data. The existing discriminative learning based PU models attempt to seek an optimal reweighting strategy for U data, so that a decent decision boundary can be found. However, given limited P data, the conventional PU models tend to suffer from overfitting when adapted to very flexible deep neural networks. In contrast, we are the first to innovate a totally new paradigm to attack the binary PU task, from perspective of generative learning by leveraging the powerful generative adversarial networks (GAN). Our generative positive-unlabeled (GenPU) framework incorporates an array of discriminators and generators that are endowed with different roles in simultaneously producing positive and negative realistic samples. We provide theoretical analysis to justify that, at equilibrium, GenPU is capable of recovering both positive and negative data distributions. Moreover, we show GenPU is generalizable and closely related to the semi-supervised classification. Given rather limited P data, experiments on both synthetic and real-world dataset demonstrate the effectiveness of our proposed framework. With infinite realistic and diverse sample streams generated from GenPU, a very flexible classifier can then be trained using deep neural networks.