Class Prior Estimation in Active Positive and Unlabeled Learning

Estimating the proportion of positive examples (i.e., the class prior) from positive and unlabeled (PU) data is an important task that facilitates learning a classifier from such data. In this paper, we explore how to tackle this problem when the observed labels were acquired via active learning. This introduces the challenge that the observed labels were not selected completely at random, which is the primary assumption underpinning existing approaches to estimating the class prior from PU data. We analyze this new setting and design an algorithm that is able to estimate the class prior for a given active learning strategy. Empirically, we show that our approach accurately recovers the true class prior on a benchmark of anomaly detection datasets and that it does so more accurately than existing methods.