Multi-Label Learning with Stronger Consistency Guarantees

• URL: http://arxiv.org/abs/2407.13746v1
• Date: Thu, 18 Jul 2024 17:51:02 GMT
• Title: Multi-Label Learning with Stronger Consistency Guarantees
• Authors: Anqi Mao, Mehryar Mohri, Yutao Zhong,
• Abstract summary: We present a detailed study of surrogate losses and algorithms for multi-label learning, supported by $H$-consistency bounds. We introduce a novel surrogate loss, multi-label logistic loss, that accounts for label correlations and benefits from label-independent $H$-consistency bounds. We prove that this family of surrogate losses benefits from $H$-consistency bounds, and thus Bayes-consistency, across any general multi-label loss.
• Score: 30.389055604165222
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a detailed study of surrogate losses and algorithms for multi-label learning, supported by $H$-consistency bounds. We first show that, for the simplest form of multi-label loss (the popular Hamming loss), the well-known consistent binary relevance surrogate suffers from a sub-optimal dependency on the number of labels in terms of $H$-consistency bounds, when using smooth losses such as logistic losses. Furthermore, this loss function fails to account for label correlations. To address these drawbacks, we introduce a novel surrogate loss, multi-label logistic loss, that accounts for label correlations and benefits from label-independent $H$-consistency bounds. We then broaden our analysis to cover a more extensive family of multi-label losses, including all common ones and a new extension defined based on linear-fractional functions with respect to the confusion matrix. We also extend our multi-label logistic losses to more comprehensive multi-label comp-sum losses, adapting comp-sum losses from standard classification to the multi-label learning. We prove that this family of surrogate losses benefits from $H$-consistency bounds, and thus Bayes-consistency, across any general multi-label loss. Our work thus proposes a unified surrogate loss framework benefiting from strong consistency guarantees for any multi-label loss, significantly expanding upon previous work which only established Bayes-consistency and for specific loss functions. Additionally, we adapt constrained losses from standard classification to multi-label constrained losses in a similar way, which also benefit from $H$-consistency bounds and thus Bayes-consistency for any multi-label loss. We further describe efficient gradient computation algorithms for minimizing the multi-label logistic loss.

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