From Local Geometry to Global Pseudo Labeling for Robust Positive Unlabeled Learning under Covariate Shift

2026-05-29

AI Summary

This work addresses the instability of traditional positive-unlabeled (PU) learning under covariate shift, where severe distributional overlap degrades performance and existing shift-detection methods rely on fully supervised labels, limiting their practicality. To overcome these challenges, the authors propose a geometry-aware PU learning framework that, for the first time, incorporates local manifold structure into PU learning. By leveraging spectral analysis and manifold learning, the method constructs local neighborhood relationships and introduces a progressive labeling mechanism that propagates information from local neighborhoods to global pseudo-labels. This enables automatic detection and exploitation of covariate shift under weak supervision. The approach demonstrates significantly enhanced robustness and generalization across diverse shift scenarios, achieving state-of-the-art performance in PU learning and rivaling fully supervised methods.

Abstract

Detecting covariate shift is critical for building reliable vision systems. While most prior work focuses on improving robustness to shift, explicitly detecting covariate shift remains underexplored. Existing approaches typically rely on fully supervised training, requiring labeled examples from both original and shifted distributions, which is often impractical. In this paper, we show that covariate shift detection can be effectively addressed with weaker supervision using Positive Unlabeled (PU) learning. However, under covariate shift, in distribution and shifted data overlap significantly, making classical PU methods unstable and sensitive to noise. To overcome this challenge, we introduce Spectral PU Neighborhood Annotation (SPUNA), a geometry aware framework that progressively discovers shifted data by leveraging the local manifold structure of visual features. Extensive experiments show that SPUNA achieves state of the art performance in PU settings and remarkably matches the performances of fully supervised methods. Moreover, our approach transfers robustly across different types of shifts, demonstrating strong generalization capabilities.

Problem

• covariate shift
• Positive Unlabeled learning
• weak supervision
• distribution shift
• shift detection

Innovation

• Positive Unlabeled Learning
• Covariate Shift Detection
• Manifold Geometry
• Pseudo Labeling
• Weak Supervision