Importance-weighted Positive-unlabeled Learning for Distribution Shift Adaptation

Positive and unlabeled (PU) learning is a fundamental task in many applications, which trains a binary classifier from only PU data. Existing PU learning methods typically assume that training and test distributions are identical. However, this assumption is often violated due to distribution shifts, and identifying shift types such as covariate and concept shifts is generally difficult. In this paper, we propose a distribution shift adaptation method for PU learning without assuming shift types by using a few PU data in the test distribution and PU data in the training distribution. Our method is based on the importance weighting, which learns the classifier in a principled manner by minimizing the importance-weighted training risk that approximates the test risk. Although existing methods require positive and negative data in both distributions for the importance weighting without assuming shift types, we theoretically show that it can be performed with only PU data in both distributions. Based on this finding, our neural network-based classifiers can be effectively trained by iterating the importance weight estimation and classifier learning. We show that our method outperforms various existing methods with seven real-world datasets.