Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention
arxiv(2023)
摘要
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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