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An Embedding Framework for Consistent Polyhedral Surrogates
Jessica Finocchiaro · Rafael Frongillo · Bo Waggoner

Wed Dec 11 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #221

We formalize and study the natural approach of designing convex surrogate loss functions via embeddings for problems such as classification or ranking. In this approach, one embeds each of the finitely many predictions (e.g. classes) as a point in \reals^d, assigns the original loss values to these points, and convexifies the loss in some way to obtain a surrogate. We prove that this approach is equivalent, in a strong sense, to working with polyhedral (piecewise linear convex) losses. Moreover, given any polyhedral loss L, we give a construction of a link function through which L is a consistent surrogate for the loss it embeds. We go on to illustrate the power of this embedding framework with succinct proofs of consistency or inconsistency of various polyhedral surrogates in the literature.

Author Information

Jessica Finocchiaro (University of Colorado Boulder)
Rafael Frongillo (CU Boulder)
Bo Waggoner (U. Colorado, Boulder)

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