A Consistent Lebesgue Measure for Multi-label Learning
This addresses the challenge of conflicting multi-label loss functions for researchers and practitioners in multi-label learning, though it appears incremental as it builds on existing surrogate loss methods.
The paper tackles the problem of non-differentiable multi-label loss functions by proposing a Consistent Lebesgue Measure-based Multi-label Learner (CLML), which achieves theoretical consistency and state-of-the-art results without needing additional components like label graphs or semantic embeddings.
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.