Learning from Positive and Unlabeled Data with Arbitrary Positive Shift
This addresses a practical limitation in PU learning for applications where positive data is biased, such as in dynamic or adversarial environments, though it is incremental by building on existing PU frameworks.
The paper tackles the problem of positive-unlabeled (PU) learning when positive data is non-representative due to shifts like temporal drift or domain changes, showing that it is possible even with arbitrary positive bias by assuming only the negative class distribution is fixed. The result includes two statistically consistent methods that demonstrate effectiveness across real-world datasets, including cases with disjoint positive supports.
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.