Estimating the class prior and posterior from noisy positives and unlabeled data
This addresses robust classification for real-world high-dimensional data with label noise, representing an incremental improvement over previous theoretical methods.
The paper tackles the problem of estimating class posterior distributions from positive-unlabeled data with noisy positive labels, developing two practical algorithms that avoid kernel density estimation for high-dimensional data and prove preservation of the class prior.
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.