Revisiting Logistic-softmax Likelihood in Bayesian Meta-Learning for Few-Shot Classification

Tianjun Ke; Haoqun Cao; Zenan Ling; Feng Zhou

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arXiv · 2310.10379

Revisiting Logistic-softmax Likelihood in Bayesian Meta-Learning for Few-Shot Classification

Tianjun Ke·Haoqun Cao·Zenan Ling·Feng Zhou

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Abstract

Meta-learning has demonstrated promising results in few-shot classification (FSC) by learning to solve new problems using prior knowledge. Bayesian methods are effective at characterizing uncertainty in FSC, which is crucial in high-risk fields. In this context, the logistic-softmax likelihood is often employed as an alternative to the softmax likelihood in multi-class Gaussian process classification due to its conditional conjugacy property. However, the theoretical property of logistic-softmax is not clear and previous research indicated that the inherent uncertainty of logistic-softmax leads to suboptimal performance. To mitigate these issues, we revisit and redesign the logistic-softmax likelihood, which enables control of the \textit{a priori} confidence level through a temperature parameter. Furthermore, we theoretically and empirically show that softmax can be viewed as a special case of logistic-softmax and logistic-softmax induces a larger family of data distribution than softmax. Utilizing modified logistic-softmax, we integrate the data augmentation technique into the deep kernel based Gaussian process meta-learning framework, and derive an analytical mean-field approximation for task-specific updates. Our approach yields well-calibrated uncertainty estimates and achieves comparable or superior results on standard benchmark datasets. Code is publicly available at \url{https://github.com/keanson/revisit-logistic-softmax}.

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BibTeX RIS

Tianjun Ke, Haoqun Cao, Zenan Ling, Feng Zhou. 2024-10-10. Revisiting Logistic-softmax Likelihood in Bayesian Meta-Learning for Few-Shot Classification. https://arxiv.org/abs/2310.10379

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