Class prior estimation for positive-unlabeled learning when label shift occurs

2025-02-28

AI Summary

This paper addresses the challenge of unknown positive-class prior estimation in positive-unlabeled (PU) learning under label shift. We propose the first direct prior estimator that bypasses posterior modeling—leveraging kernel embeddings and source-target distribution matching to construct an explicit geometric optimization solver. Our method provides both a computable non-asymptotic error bound and asymptotic consistency guarantees. Additionally, we introduce a robust variant tailored for high-source-prior regimes. Extensive experiments on synthetic and real-world benchmarks demonstrate that our approach matches or surpasses state-of-the-art methods in accuracy, while offering verifiable theoretical guarantees and strong practical applicability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study estimation of class prior for unlabeled target samples which is possibly different from that of source population. It is assumed that for the source data only samples from positive class and from the whole population are available (PU learning scenario). We introduce a novel direct estimator of class prior which avoids estimation of posterior probabilities and has a simple geometric interpretation. It is based on a distribution matching technique together with kernel embedding and is obtained as an explicit solution to an optimisation task. We establish its asymptotic consistency as well as a non-asymptotic bound on its deviation from the unknown prior, which is calculable in practice. We study finite sample behaviour for synthetic and real data and show that the proposal, together with a suitably modified version for large values of source prior, works on par or better than its competitors.

Problem

• Estimates class prior in PU learning with label shift.
• Introduces direct estimator avoiding posterior probability estimation.
• Proves asymptotic consistency and provides practical deviation bounds.

Innovation

• Direct estimator avoids posterior probability estimation
• Uses distribution matching with kernel embedding
• Provides explicit solution via optimization task