Cardinality-Aware Top-k Classification: Balancing Accuracy and Prediction Size

This paper presents a detailed study of top-k classification, where the goal is to predict the k most probable classes for an input. It demonstrates that several prevalent surrogate loss functions in multi-class classification, such as comp-sum and constrained losses, admit strong H-consistency bounds with respect to the top-k loss. To address the trade-off between accuracy and cardinality k, the paper introduces cardinality-aware loss functions through instance-dependent cost-sensitive learning, and derives novel cost-sensitive surrogate losses that also benefit from H-consistency guarantees. Minimizing these losses leads to new cardinality-aware algorithms for top-k classification, which are shown to outperform standard top-k classifiers on benchmark datasets.