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
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.