Top-$k$ Classification and Cardinality-Aware Prediction
<|reference_start|>Top-$k$ Classification and Cardinality-Aware Prediction: 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.<|reference_end|>
@article{mao2024top-$k$,
    title={Top-$k$ Classification and Cardinality-Aware Prediction},
    author={Anqi Mao, Mehryar Mohri, Yutao Zhong},
    journal={arXiv preprint arXiv:2403.19625},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19625},
    primaryClass={cs.LG stat.ML}
}