Positive and Unlabeled (PU) learning aims to train a suitable classifier simply based on a set of positive data and unlabeled data. Existing PU methods usually follow a discriminative framework and yield limited classification performance, because the lack of explicit negative labels poses a great barrier in training a discriminative PU model. To address the challenge of limited supervisory information faced by discriminative PU methods, this paper introduces generative operation to PU learning in addition to the conventional discriminative operation, and proposes a novel algorithm dubbed "Discriminative-Generative Positive and Unlabeled Learning" (DGPU). Specifically, our proposed DGPU consists of a data generation stage and a discriminative annotation stage, which can benefit from each other in an iterative manner. In data generation stage, we employ a tailored diffusion model to generate high-quality negative examples and positive examples to efficiently enrich the supervisory information. In discriminative annotation stage, the classifier is further refined on the initial and generated training data. To the best of our knowledge, this study represents the first attempt to integrate diffusion models into PU learning to make generative model and discriminative model benefit from each other in a collaborative way. Thanks to this, our proposed DGPU significantly outperforms existing PU methods across a wide range of synthetic and real-world benchmark datasets. In particular, our DGPU is almost comparable to the fully supervised counterpart, and improves the test accuracy of existing state-of-the-art methods by 3.89% and 2.56% on CIFAR-10 and CelebA datasets, respectively.

Positive and unlabeled (PU) learning aims to train a suitable classifier simply based on a set of positive data and unlabeled data. The state-of-the-art methods usually formulate PU learning as a cost-sensitive learning problem, in which every unlabeled example is treated as negative with modified class weights. However, existing methods fail to generate high-quality data representations, which brings about negative-prediction preference and performance decline. To overcome this problem, this article proposes a novel algorithm dubbed weighted contrastive learning with hard negative mining for positive and unlabeled learning (termed WConPU), which specifically designs a new prototypical contrastive strategy for gaining discriminative representations for PU learning. Specifically, our proposed WConPU consists of a contrastive learning (CL) module and a classifier training module, which can benefit from each other in an iterative manner. Moreover, a novel weighted contrastive objective function equipped with a prototype-based hard negative mining module is proposed to further enhance the representation quality. Theoretically, we show that our WConPU can be justified from the perspective of the expectation-maximization (EM) algorithm. Empirically, we compare our method with state-of-the-art PU algorithms on a wide range of real-world benchmark datasets, and the experimental results firmly demonstrate the advantage of our proposed method over the existing PU learning approaches.