Queryable and Interpretable PU Learning Through Probabilistic Circuits

Abstract

We introduce a novel concept learning scenario that involves only positive and unlabeled (PU) data and focuses on interpretable models. Our scenario is motivated by a real-world application learning concepts for music playlists (e.g., ‘relaxing music’). These concepts must be understood by humans and used as database queries. We demonstrate that probabilistic circuits offer a compelling solution for PU learning as they can effectively learn to represent joint probability distributions without the need for negative examples. However, achieving interpretability and seamless conversion into database queries presents additional challenges. To address these, we propose a novel approach that transforms a learned probabilistic circuit into a logic-based discriminative model. Notably, this is the first study to investigate probabilistic circuits in a PU learning framework, contributing two key innovations: (1) a new description length metric called aggregated entropy as a measure for interpretability; and (2) PUTPUT, an algorithm designed to prune low-probability regions from the circuit before converting it into a logic-based model, optimizing for both F $_1$ 1 -score and aggregated entropy.