Original title: Optimality conditions for maximizers of the information divergence from an exponential family
Translated title: Optimální podmínky pro maximalizaci informační divergence exponenciální rodiny
Authors: Matúš, František
Document type: Papers
Conference/Event: WUPES 2006, Mikulov (CZ), 2006-09-16 / 2006-09-20
Year: 2006
Language: eng
Abstract: [eng] [cze]
The information divergence of a probability measure P from an exponential family E over a finite set is defined as infimum of the divergences of P from Q subject to Q in E. All directional derivatives of the divergence from E are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for P to be a maximizer of the divergence from E are presented, including new ones when P is not projectable to E. Informační divergence pravděpodobnostní míry P od exponenciální rodiny se definuje jako infimum divergencí P od Q v E. Byly spočteny směrové derivace této divergence pomocí nových výsledků o konjugaci log-Lapaceovy transformace. Byly formulovány nové nutné podmínky prvního řádu proto, aby P byla maximalizátorem této divergence
Keywords: cumulant generating function; exponential family; information projection; Kullback-Leibler divergence; log-Laplace transform; relative entropy
Project no.: CEZ:AV0Z10750506 (CEP), IAA100750603 (CEP)
Funding provider: GA AV ČR
Host item entry: WUPES '06 Proceedings of 7th Workshop on Uncertainty Processing, ISBN 80-245-1079-0

Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0134694

Permalink: http://www.nusl.cz/ntk/nusl-35542


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