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# Class-prior Estimation for Learning from Positive and Unlabeled Data

*Asian Conference on Machine Learning*, PMLR 45:221-236, 2016.

#### Abstract

We consider the problem of estimating the \emphclass 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, and establish its uniform deviation bound and estimation error bound. Finally, we experimentally demonstrate the usefulness of the proposed method.