Poster
Tue Dec 07 04:30 PM -- 06:00 PM (PST)
Unifying lower bounds on prediction dimension of convex surrogates
[
OpenReview]
The convex consistency dimension of a supervised learning task is the lowest prediction dimension such that there exists a convex surrogate that is consistent for the given task. We present a new tool based on property elicitation, -flats, for lower-bounding convex consistency dimension. This tool unifies approaches from a variety of domains, including continuous and discrete prediction problems. We use -flats to obtain a new lower bound on the convex consistency dimension of risk measures, resolving an open question due to Frongillo and Kash (NeurIPS 2015). In discrete prediction settings, we show that the -flats approach recovers and even tightens previous lower bounds using feasible subspace dimension.