A no-regret generalization of hierarchical softmax to extreme multi-label classification

Extreme multi-label classification (XMLC) is a problem of tagging an instance with a small subset of relevant labels chosen from an extremely large pool of possible labels. Large label spaces can be efficiently handled by organizing labels as a tree, like in the hierarchical softmax (HSM) approach commonly used for multi-class problems. In this paper, we investigate probabilistic label trees (PLTs) that have been recently devised for tackling XMLC problems. We show that PLTs are a no-regret multi-label generalization of HSM when precision@$k$ is used as a model evaluation metric. Critically, we prove that pick-one-label heuristic---a reduction technique from multi-label to multi-class that is routinely used along with HSM---is not consistent in general.