标题： 一种多标签学习的相容勒贝格测度 显示英文标题

标题： A Consistent Lebesgue Measure for Multi-label Learning

摘要： 多标签损失函数通常是不可微的，需要替代损失函数进行基于梯度的优化。 替代损失函数的一致性尚未得到证明，并且由于多标签损失函数的冲突性质而加剧。 为了直接从多个相关但可能冲突的多标签损失函数中学习，我们提出了一种基于勒贝格测度的多标签学习器（CLML），并证明在贝叶斯风险框架下，CLML可以达到理论一致性。 实证证据支持我们的理论，表明：（1）CLML可以一致地达到最先进结果；（2）主要性能因素是勒贝格测度设计，因为CLML优化了一个更简单的前馈模型，而无需额外的标签图、基于扰动的条件或语义嵌入；（3）对结果的分析不仅区分了CLML的有效性，还突显了替代损失函数与期望损失函数之间的不一致性。 显示英文摘要

摘要： 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.