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Unifying lower bounds on prediction dimension of convex surrogates
Jessica Finocchiaro · Rafael Frongillo · Bo Waggoner

Tue Dec 07 04:30 PM -- 06:00 PM (PST) @ None #None
The convex consistency dimension of a supervised learning task is the lowest prediction dimension $d$ such that there exists a convex surrogate $L : \mathbb{R}^d \times \mathcal Y \to \mathbb R$ that is consistent for the given task. We present a new tool based on property elicitation, $d$-flats, for lower-bounding convex consistency dimension. This tool unifies approaches from a variety of domains, including continuous and discrete prediction problems. We use $d$-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 $d$-flats approach recovers and even tightens previous lower bounds using feasible subspace dimension.

Author Information

Jessica Finocchiaro (University of Colorado Boulder)
Rafael Frongillo (University of Colorado Boulder)
Bo Waggoner

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