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

Detecting covariate shift is critical for building reliable vi-sion systems. While most prior work focuses on improving robustness toshift, explicitly detecting covariate shift remains underexplored. Existingapproaches typically rely on fully supervised training, requiring labeledexamples from both original and shifted distributions, which is often im-practical. In this paper, we show that covariate shift detection can beeffectively addressed with weaker supervision using Positive–Unlabeled(PU) learning. However, under covariate shift, in-distribution and shifteddata overlap significantly, making classical PU methods unstable and sen-sitive to noise. To overcome this challenge, we introduce Spectral PUNeighborhood Annotation (S-PUNA), a geometry-aware frame-work that progressively discovers shifted data by leveraging the localmanifold structure of visual features. Extensive experiments show thatS-PUNA achieves state-of-the-art performance in PU settings and re-markably matches the performance of fully supervised methods. More-over, our approach transfers robustly across different types of shifts,demonstrating strong generalization capabilities. Code is available athttps://github.com/fira7s/S-PUNA.