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The goal in extreme multi-label classification (XMC) is to tag an instancewith a small subset of relevant labels from an extremely large set of possiblelabels. In addition to the computational burden arising from large number oftraining instances, features and labels, problems in XMC are faced with twostatistical challenges, (i) large number of 'tail-labels' -- those which occurvery infrequently, and (ii) missing labels as it is virtually impossible tomanually assign every relevant label to an instance. In this work, we derive anunbiased estimator for general formulation of loss functions which decomposeover labels, and then infer the forms for commonly used loss functions such ashinge- and squared-hinge-loss and binary cross-entropy loss. We show that thederived unbiased estimators, in the form of appropriate weighting factors, canbe easily incorporated in state-of-the-art algorithms for extremeclassification, thereby scaling to datasets with hundreds of thousand labels.However, empirically, we find a slightly altered version that gives morerelative weight to tail labels to perform even better. We suspect is due to thelabel imbalance in the dataset, which is not explicitly addressed by ourtheoretically derived estimator. Minimizing the proposed loss functions leadsto significant improvement over existing methods (up to 20% in some cases) onbenchmark datasets in XMC.

Unbiased Loss Functions for Extreme Classification With Missing Labels