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Learning from positive and unlabeled data or PU learning is the setting where a learner only has access to positive examples and unlabeled data. The assumption is that the unlabeled data can contain both positive and negative examples. This…

Machine Learning · Computer Science 2020-05-19 Jessa Bekker , Jesse Davis

We propose a new method of learning from positive and unlabeled (PU) examples in highly imbalanced datasets. Many real-world problems, such as disease gene identification, targeted marketing, fraud detection, and recommender systems, are…

Machine Learning · Computer Science 2026-05-15 Elias Zavitsanos , Georgios Paliouras

We consider a problem of learning a binary classifier only from positive data and unlabeled data (PU learning) and estimating the class-prior in unlabeled data under the case-control scenario. Most of the recent methods of PU learning…

Machine Learning · Computer Science 2018-09-18 Masahiro Kato , Liyuan Xu , Gang Niu , Masashi Sugiyama

We address learning from positive and unlabeled (PU) data, a common setting in which only some positives are labeled and the rest are mixed with negatives. Classical exponential tilting models guarantee identifiability by assuming a linear…

Methodology · Statistics 2025-08-19 Peijun Sang , Yifan Sun , Qinglong Tian , Donglin Zeng , Pengfei Li

From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, empirical risks on training data will go…

Machine Learning · Computer Science 2017-11-07 Ryuichi Kiryo , Gang Niu , Marthinus C. du Plessis , Masashi Sugiyama

In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by…

Machine Learning · Computer Science 2014-11-25 Cho-Jui Hsieh , Nagarajan Natarajan , Inderjit S. Dhillon

The goal of positive-unlabeled (PU) learning is to train a binary classifier on the basis of training data containing positive and unlabeled instances, where unlabeled observations can belong either to the positive class or to the negative…

Machine Learning · Statistics 2024-04-02 Paweł Teisseyre , Konrad Furmańczyk , Jan Mielniczuk

Learning binary classifiers from positive and unlabeled data (PUL) is vital in many real-world applications, especially when verifying negative examples is difficult. Despite the impressive empirical performance of recent PUL methods,…

Machine Learning · Computer Science 2024-10-14 Xinrui Wang , Wenhai Wan , Chuanxin Geng , Shaoyuan LI , Songcan Chen

We present a novel approach to learn binary classifiers when only positive and unlabeled instances are available (PU learning). This problem is routinely cast as a supervised task with label noise in the negative set. We use an ensemble of…

Machine Learning · Statistics 2015-02-13 Marc Claesen , Frank De Smet , Johan A. K. Suykens , Bart De Moor

Learning from Multi-Positive and Unlabeled (MPU) data has gradually attracted significant attention from practical applications. Unfortunately, the risk of MPU also suffer from the shift of minimum risk, particularly when the models are…

Machine Learning · Computer Science 2024-12-04 Zhongnian Li , Meng Wei , Peng Ying , Xinzheng Xu

Motivated by applications in protein function prediction, we consider a challenging supervised classification setting in which positive labels are scarce and there are no explicit negative labels. The learning algorithm must thus select…

Machine Learning · Computer Science 2019-01-28 Marco Frasca , Nicolò Cesa-Bianchi

Learning from positive and unlabeled (PU) data is a setting where the learner only has access to positive and unlabeled samples while having no information on negative examples. Such PU setting is of great importance in various tasks such…

Machine Learning · Computer Science 2022-09-07 Emilio Dorigatti , Jonas Schweisthal , Bernd Bischl , Mina Rezaei

Positive-Unlabeled (PU) learning addresses classification problems where only a subset of positive examples is labeled and the remaining data is unlabeled, making explicit negative supervision unavailable. Existing PU methods often rely on…

Machine Learning · Computer Science 2026-01-26 Vasileios Sevetlidis , George Pavlidis , Antonios Gasteratos

This paper is concerned with learning of mixture regression models for individuals that are measured repeatedly. The adjective "unsupervised" implies that the number of mixing components is unknown and has to be determined, ideally by data…

Methodology · Statistics 2018-01-09 Peirong Xu , Heng Peng , Tao Huang

In causal inference, whether through randomized controlled trials or observational studies, access to both treated and control units is essential for estimating the effect of a treatment on an outcome of interest. When treatment assignment…

A common approach in positive-unlabeled learning is to train a classification model between labeled and unlabeled data. This strategy is in fact known to give an optimal classifier under mild conditions; however, it results in biased…

Machine Learning · Statistics 2017-02-03 Shantanu Jain , Martha White , Predrag Radivojac

Positive-unlabeled learning (PU learning) is known as a special case of semi-supervised binary classification where only a fraction of positive examples are labeled. The challenge is then to find the correct classifier despite this lack of…

Statistics Theory · Mathematics 2022-01-19 Olivier Coudray , Christine Keribin , Pascal Massart , Patrick Pamphile

We introduce a new observational setting for Positive Unlabeled (PU) data where the observations at prediction time are also labeled. This occurs commonly in practice -- we argue that the additional information is important for prediction,…

Machine Learning · Statistics 2024-07-16 Jan Mielniczuk , Adam Wawrzeńczyk

This paper proposes a novel pseudo-labeling method for medical image segmentation that can perform learning on ``individual images'' to select effective pseudo-labels. We introduce Positive and Unlabeled Learning (PU learning), which uses…

Computer Vision and Pattern Recognition · Computer Science 2025-08-12 Takehiro Yamane , Itaru Tsuge , Susumu Saito , Ryoma Bise

We study the problem of learning from positive and unlabeled (PU) data in the federated setting, where each client only labels a little part of their dataset due to the limitation of resources and time. Different from the settings in…

Machine Learning · Computer Science 2022-08-16 Xinyang Lin , Hanting Chen , Yixing Xu , Chao Xu , Xiaolin Gui , Yiping Deng , Yunhe Wang