NDLI: The key theorem and the bounds on the rate of uniform convergence of learning theory on Sugeno measure space

Content Provider	Springer Nature Link
Author	Ha, Minghu Li, Yan Li, Jia Tian, Dazeng
Copyright Year	2006
Abstract	Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of g $_{ λ }$ random variable and its distribution function, expected value, and variance are then presented. Markov inequality, Chebyshev’s inequality and the Khinchine’s Law of Large Numbers on Sugeno measure space are also proven. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of ERM principle on Sugeno measure space are proposed. According to these properties and concepts, the key theorem of learning theory, the bounds on the rate of convergence of learning process and the relations between these bounds and capacity of the set of functions on Sugeno measure space are given.
Starting Page	372
Ending Page	385
Page Count	14
File Format	PDF
ISSN	10092757
Journal	Science in China Series : Information Sciences
Volume Number	49
Issue Number	3
e-ISSN	18622836
Language	English
Publisher	Science in China Press
Publisher Date	2006-01-01
Publisher Place	Beijing
Access Restriction	Subscribed
Subject Keyword	Sugeno measure the empirical risk minimization principle the key theorem the bounds on the rate of uniform convergence Information Systems and Communication Service
Content Type	Text
Resource Type	Article
Subject	Computer Science

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The key theorem and the bounds on the rate of uniform convergence of learning theory on Sugeno measure space