A Flexible Procedure for Mixture Proportion Estimation in Positive-Unlabeled Learning
This work addresses a key bottleneck in PU learning for applications like bioinformatics, but it is incremental as it builds on prior methods with a flexible approach.
The authors tackled the problem of mixture proportion estimation in positive-unlabeled learning by proposing a flexible framework that reduces it to a one-dimensional task using a probabilistic classifier and methods from multiple testing literature. They proved consistency for two estimators, developed tuning-free implementations, and showed competitive performance on simulated waveform data and a protein signaling problem, with results indicating effectiveness comparable to existing approaches.
Positive--unlabeled (PU) learning considers two samples, a positive set P with observations from only one class and an unlabeled set U with observations from two classes. The goal is to classify observations in U. Class mixture proportion estimation (MPE) in U is a key step in PU learning. Blanchard et al. [2010] showed that MPE in PU learning is a generalization of the problem of estimating the proportion of true null hypotheses in multiple testing problems. Motivated by this idea, we propose reducing the problem to one dimension via construction of a probabilistic classifier trained on the P and U data sets followed by application of a one--dimensional mixture proportion method from the multiple testing literature to the observation class probabilities. The flexibility of this framework lies in the freedom to choose the classifier and the one--dimensional MPE method. We prove consistency of two mixture proportion estimators using bounds from empirical process theory, develop tuning parameter free implementations, and demonstrate that they have competitive performance on simulated waveform data and a protein signaling problem.