# Top-$k$ Classification and Cardinality-Aware Prediction

Source: [Top-$k$ Classification and Cardinality-Aware Prediction](<https://www.sota2.com/research/paper/68fa72ae1e209131cea57d51>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T02:31:50.592Z

Authors: Anqi Mao, Mehryar Mohri, Yutao Zhong

Published: 2024-03-28T17:45:03.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2403.19625>)

[PDF](<https://arxiv.org/pdf/2403.19625.pdf>)