A Consistent Lebesgue Measure for Multi-label Learning

Kaan Demir; Bach Nguyen; Bing Xue; Mengjie Zhang

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arXiv · 2402.00324

A Consistent Lebesgue Measure for Multi-label Learning

Kaan Demir·Bach Nguyen·Bing Xue·Mengjie Zhang

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Abstract

Multi-label loss functions are usually non-differentiable, requiring surrogate loss functions for gradient-based optimisation. The consistency of surrogate loss functions is not proven and is exacerbated by the conflicting nature of multi-label loss functions. To directly learn from multiple related, yet potentially conflicting multi-label loss functions, we propose a Consistent Lebesgue Measure-based Multi-label Learner (CLML) and prove that CLML can achieve theoretical consistency under a Bayes risk framework. Empirical evidence supports our theory by demonstrating that: (1) CLML can consistently achieve state-of-the-art results; (2) the primary performance factor is the Lebesgue measure design, as CLML optimises a simpler feedforward model without additional label graph, perturbation-based conditioning, or semantic embeddings; and (3) an analysis of the results not only distinguishes CLML's effectiveness but also highlights inconsistencies between the surrogate and the desired loss functions.

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BibTeX RIS

Kaan Demir, Bach Nguyen, Bing Xue, Mengjie Zhang. 2024-02-01. A Consistent Lebesgue Measure for Multi-label Learning. https://arxiv.org/abs/2402.00324

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