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Representation of Quasi-Monotone Functionals by Families of Separating Hyperplanes

2015/08/21 by Ingo Steinwart, Steinwart, Ingo
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Statistics Theory (math.ST) #math.FA #math.OC #math.ST #stat.ML #stat.TH

paper · pdf · doi:10.48550/arxiv.1508.05249

23 pages

arxiv created 2015/08/21 · arxiv updated 2015/08/24

Abstract

We characterize when the level sets of a continuous quasi-monotone functional defined on a suitable convex subset of a normed space can be uniquely represented by a family of bounded continuous functionals. Furthermore, we investigate how regularly these functionals depend on the parameterizing level. Finally, we show how this question relates to the recent problem of property elicitation that simultaneously attracted interest in machine learning, statistical evaluation of forecasts, and finance.

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