Divergences, surrogate loss functions and experimental design

In this paper, we provide a general theorem that establishes a correspondence betweensurrogate loss functions in classification and the family of f-divergences. Moreover, we provide constructive procedures for determining the f-divergence induced by a given surrogate loss, and conversely for finding all surrogate loss functions that realize a given f-divergence. Next we introduce the notion of universal equivalence among loss functions and corresponding f-divergences, and provide necessary andsufficient conditions for universal equivalence to hold. These ideas have applications to classification problems that also involve a component ofexperiment design; in particular, we leverage our results to prove consistency of a procedure for learning a classifier under decentralization requirements.