Top-$k$ Classification and Cardinality-Aware Prediction
This addresses the problem of improving multi-class classification accuracy while controlling prediction size for machine learning practitioners, though it appears incremental as it builds on existing loss functions.
The paper tackles top-k classification by showing that existing surrogate loss functions have H-consistency bounds and introducing cardinality-aware loss functions with new algorithms, demonstrating effectiveness on multiple datasets including CIFAR-100 and ImageNet.
We present a detailed study of top-$k$ classification, the task of predicting the $k$ most probable classes for an input, extending beyond single-class prediction. We demonstrate that several prevalent surrogate loss functions in multi-class classification, such as comp-sum and constrained losses, are supported by $H$-consistency bounds with respect to the top-$k$ loss. These bounds guarantee consistency in relation to the hypothesis set $H$, providing stronger guarantees than Bayes-consistency due to their non-asymptotic and hypothesis-set specific nature. To address the trade-off between accuracy and cardinality $k$, we further introduce cardinality-aware loss functions through instance-dependent cost-sensitive learning. For these functions, we derive cost-sensitive comp-sum and constrained surrogate losses, establishing their $H$-consistency bounds and Bayes-consistency. Minimizing these losses leads to new cardinality-aware algorithms for top-$k$ classification. We report the results of extensive experiments on CIFAR-100, ImageNet, CIFAR-10, and SVHN datasets demonstrating the effectiveness and benefit of these algorithms.