The Convexity and Design of Composite Multiclass Losses
This work addresses theoretical foundations for loss function design in multiclass classification, but it appears incremental as it builds on existing composite loss frameworks.
The paper tackles the problem of designing convex composite loss functions for multiclass prediction by establishing conditions for their convexity and showing how this representation enables the creation of loss families with identical Bayes risk.
We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk.