On the Consistency of Max-Margin Losses
This addresses a foundational problem in machine learning for structured prediction tasks, offering a more robust loss function, though it is incremental in refining an existing concept.
The paper tackles the inconsistency of Max-Margin losses in multi-label structured prediction, showing they are only consistent under restrictive conditions like tree graph distances, and introduces Restricted-Max-Margin as a corrected loss that ensures consistency under milder conditions.
The foundational concept of Max-Margin in machine learning is ill-posed for output spaces with more than two labels such as in structured prediction. In this paper, we show that the Max-Margin loss can only be consistent to the classification task under highly restrictive assumptions on the discrete loss measuring the error between outputs. These conditions are satisfied by distances defined in tree graphs, for which we prove consistency, thus being the first losses shown to be consistent for Max-Margin beyond the binary setting. We finally address these limitations by correcting the concept of Max-Margin and introducing the Restricted-Max-Margin, where the maximization of the loss-augmented scores is maintained, but performed over a subset of the original domain. The resulting loss is also a generalization of the binary support vector machine and it is consistent under milder conditions on the discrete loss.