Estimating the class prior and posterior from noisy positives and unlabeled data

TL;DR

This paper introduces robust classification algorithms for positive-unlabeled data that effectively handle label noise and high-dimensionality, enabling accurate estimation of class priors and posteriors in practical scenarios.

Contribution

The authors develop two practical algorithms that explicitly model label noise and use univariate transforms, improving robustness and applicability over previous theoretical methods.

Findings

Algorithms perform well on high-dimensional noisy data

Univariate transforms preserve class prior

Avoidance of kernel density estimation in high dimensions

Abstract

We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contributions remain theoretical, performing poorly on real high-dimensional data that is typically contaminated with noise. We build on this previous work to develop two practical classification algorithms that explicitly model the noise in the positive labels and utilize univariate transforms built on discriminative classifiers. We prove that these univariate transforms preserve the class prior, enabling estimation in the univariate space and avoiding kernel density estimation for high-dimensional data. The theoretical development and both parametric and nonparametric algorithms proposed here constitutes an important step towards wide-spread use of robust classification algorithms for positive-unlabeled data.