Active learning and the Saerens-Latinne-Decaestecker algorithm: an evaluation

The Saerens-Latinne-Decaestecker (SLD) algorithm is a method whose goal is improving the quality of the posterior probabilities (or simply "posteriors") returned by a probabilistic classifier in scenarios characterized by prior probability shift (PPS) between the training set and the unlabelled ("test") set. This is an important task, (a) because posteriors are of the utmost importance in downstream tasks such as, e.g., multiclass classification and cost-sensitive classification, and (b) because PPS is ubiquitous in many applications. In this paper we explore whether using SLD can indeed improve the quality of posteriors returned by a classifier trained via active learning (AL), a class of machine learning (ML) techniques that indeed tend to generate substantial PPS. Specifically, we target AL via relevance sampling (ALvRS) and AL via uncertainty sampling (ALvUS), two AL techniques that are very well-known especially because, due to their low computational cost, are suitable to being applied in scenarios characterized by large datasets. We present experimental results obtained on the RCV1-v2 dataset, showing that SLD fails to deliver better-quality posteriors with both ALvRS and ALvUS, thus contradicting previous findings in the literature, and that this is due not to the amount of PPS that these techniques generate, but to how the examples they prioritize for annotation are distributed.