Class-prior Estimation for Learning from Positive and Unlabeled Data

TL;DR

This paper introduces a method to accurately estimate the class prior in unlabeled datasets using only positive samples, employing penalized divergences for efficient and reliable estimation.

Contribution

It proposes a novel approach that estimates class prior with positive samples alone by using penalized divergences, eliminating the need for negative samples.

Findings

The method accurately estimates class prior in experiments.

The use of penalized $L_1$-distance yields an efficient algorithm.

Theoretical analysis confirms consistency and stability.

Abstract

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.