Class-prior estimation for learning from positive and unlabeled data

We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such a...

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Bibliographic Details
Published in:Machine learning 2017-04, Vol.106 (4), p.463-492
Main Authors: du Plessis, Marthinus C., Niu, Gang, Sugiyama, Masashi
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Computational efficiency
Computer Science
Consistency
Control
Error analysis
Estimating techniques
Exact solutions
Machine learning
Mechatronics
Natural Language Processing (NLP)
Robotics
Simulation and Modeling
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Summary:We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such an additional labeled dataset is often not available. In this paper, we show that, with additional samples coming only from the positive class, the class prior of the unlabeled dataset can be estimated correctly. Our key idea is to use properly penalized divergences for model fitting to cancel the error caused by the absence of negative samples. We further show that the use of the penalized L 1 -distance gives a computationally efficient algorithm with an analytic solution. The consistency, stability, and estimation error are theoretically analyzed. Finally, we experimentally demonstrate the usefulness of the proposed method.
ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-016-5604-6