Learning from Positive and Unlabeled Data with Arbitrary Positive Shift

TL;DR

This paper develops methods for positive-unlabeled learning that remain effective even when positive data is biased or non-representative, by focusing on the fixed negative class distribution and introducing new risk estimation techniques.

Contribution

It introduces two novel, statistically consistent methods for PU learning under arbitrary positive bias, relaxing the common assumption of positive data representativeness.

Findings

Methods outperform existing approaches on real-world datasets.

Effective under various positive bias scenarios, including disjoint supports.

Addresses overfitting in PU risk estimation.

Abstract

Positive-unlabeled (PU) learning trains a binary classifier using only positive and unlabeled data. A common simplifying assumption is that the positive data is representative of the target positive class. This assumption rarely holds in practice due to temporal drift, domain shift, and/or adversarial manipulation. This paper shows that PU learning is possible even with arbitrarily non-representative positive data given unlabeled data from the source and target distributions. Our key insight is that only the negative class's distribution need be fixed. We integrate this into two statistically consistent methods to address arbitrary positive bias - one approach combines negative-unlabeled learning with unlabeled-unlabeled learning while the other uses a novel, recursive risk estimator. Experimental results demonstrate our methods' effectiveness across numerous real-world datasets and forms of positive bias, including disjoint positive class-conditional supports. Additionally, we propose a general, simplified approach to address PU risk estimation overfitting.