Risk bounds for infinitely divisible distribution

Zhang, C; Tao, D

Risk bounds for infinitely divisible distribution

Zhang, C Tao, D

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Publication Type:: Conference Proceeding
Citation:: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011, 2011, pp. 796 - 803
Issue Date:: 2011-09-29

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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	2011-09-29	en_US
dc.identifier.citation	Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011, 2011, pp. 796 - 803	en_US
dc.identifier.uri	http://hdl.handle.net/10453/120479
dc.description.abstract	In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation inequalities, we obtain the risk bounds based on the covering number for the ID distribution. Finally, we analyze the asymptotic convergence of the risk bound derived from one of the two deviation inequalities and show that the convergence rate of the bound is faster than the result for the generic i.i.d. empirical process (Mendelson, 2003).	en_US
dc.relation.ispartof	Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011	en_US
dc.title	Risk bounds for infinitely divisible distribution	en_US
dc.type	Conference Proceeding
utslib.for	0801 Artificial Intelligence and Image Processing	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	closed_access
pubs.publication-status	Published	en_US

Abstract:

In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation inequalities, we obtain the risk bounds based on the covering number for the ID distribution. Finally, we analyze the asymptotic convergence of the risk bound derived from one of the two deviation inequalities and show that the convergence rate of the bound is faster than the result for the generic i.i.d. empirical process (Mendelson, 2003).

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