Generalization bound for infinitely divisible empirical process

Zhang, C; Tao, D

Generalization bound for infinitely divisible empirical process

Zhang, C Tao, D

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Publication Type:: Conference Proceeding
Citation:: Journal of Machine Learning Research, 2011, 15 pp. 864 - 872
Issue Date:: 2011-12-01

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Field	Value	Language
dc.contributor.author	Zhang, C	en_US
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.date.issued	2011-12-01	en_US
dc.identifier.citation	Journal of Machine Learning Research, 2011, 15 pp. 864 - 872	en_US
dc.identifier.issn	1532-4435	en_US
dc.identifier.uri	http://hdl.handle.net/10453/19125
dc.description.abstract	In this paper, we study the generalization bound for an empirical process of samples independently drawn from an infinitely divisible (ID) distribution, which is termed as the ID empirical process. In particular, based on a martingale method, we develop deviation inequalities for the sequence of random variables of an ID distribution. By applying the obtained deviation inequalities, we then show the generalization bound for ID empirical process based on the annealed Vapnik-Chervonenkis (VC) entropy. Afterward, according to Sauer's lemma, we get the generalization bound for ID empirical process based on the VC dimension. Finally, by using a resulted result bound, we analyze the asymptotic convergence of ID empirical process and show that the convergence rate of ID empirical process can reach O (( ΔF(2N)N) 11.3) and it is faster than the results of the generic i.i.d. empirical process (Vapnik, 1999). Copyright 2011 by the authors.	en_US
dc.relation.ispartof	Journal of Machine Learning Research	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Generalization bound for infinitely divisible empirical process	en_US
dc.type	Conference Proceeding
utslib.citation.volume	15	en_US
utslib.for	080199 Artificial Intelligence and Image Processing not elsewhere classified	en_US
utslib.for	08 Information and Computing Sciences	en_US
utslib.for	17 Psychology and Cognitive Sciences	en_US
dc.location.activity	Ft. Lauderdale, FL, USA	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access
pubs.publication-status	Published	en_US
pubs.volume	15	en_US

Abstract:

In this paper, we study the generalization bound for an empirical process of samples independently drawn from an infinitely divisible (ID) distribution, which is termed as the ID empirical process. In particular, based on a martingale method, we develop deviation inequalities for the sequence of random variables of an ID distribution. By applying the obtained deviation inequalities, we then show the generalization bound for ID empirical process based on the annealed Vapnik-Chervonenkis (VC) entropy. Afterward, according to Sauer's lemma, we get the generalization bound for ID empirical process based on the VC dimension. Finally, by using a resulted result bound, we analyze the asymptotic convergence of ID empirical process and show that the convergence rate of ID empirical process can reach O (( ΔF(2N)N) 11.3) and it is faster than the results of the generic i.i.d. empirical process (Vapnik, 1999). Copyright 2011 by the authors.

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http://hdl.handle.net/10453/19125