Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention

• URL: http://arxiv.org/abs/2310.14770v2
• Date: Sun, 31 Mar 2024 09:37:14 GMT
• Title: Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention
• Authors: Anqi Mao, Mehryar Mohri, Yutao Zhong,
• Abstract summary: We introduce new families of surrogate losses for the abstention loss function. We prove strong non-asymptotic and hypothesis set-specific consistency guarantees for these surrogate losses. Our results show that the relative performance of the state-of-the-art score-based surrogate losses can vary across datasets.
• Score: 30.389055604165222
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning with abstention is a key scenario where the learner can abstain from making a prediction at some cost. In this paper, we analyze the score-based formulation of learning with abstention in the multi-class classification setting. We introduce new families of surrogate losses for the abstention loss function, which include the state-of-the-art surrogate losses in the single-stage setting and a novel family of loss functions in the two-stage setting. We prove strong non-asymptotic and hypothesis set-specific consistency guarantees for these surrogate losses, which upper-bound the estimation error of the abstention loss function in terms of the estimation error of the surrogate loss. Our bounds can help compare different score-based surrogates and guide the design of novel abstention algorithms by minimizing the proposed surrogate losses. We experimentally evaluate our new algorithms on CIFAR-10, CIFAR-100, and SVHN datasets and the practical significance of our new surrogate losses and two-stage abstention algorithms. Our results also show that the relative performance of the state-of-the-art score-based surrogate losses can vary across datasets.

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