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Extremum Problems With Total Variation Distance and Their Applications
KTH, School of Electrical Engineering (EES), Automatic Control.
2014 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 9, 2353-2368 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to investigate extremum problems with pay-off being the total variation distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures, and vice-versa; that is, with the roles of total variation metric and linear functional interchanged. Utilizing concepts from signed measures, the extremum probability measures of such problems are obtained in closed form, by identifying the partition of the support set and the mass of these extremum measures on the partition. The results are derived for abstract spaces; specifically, complete separable metric spaces known as Polish spaces, while the high level ideas are also discussed for denumerable spaces endowed with the discrete topology. These extremum problems often arise in many areas, such as, approximating a family of probability distributions by a given probability distribution, maximizing or minimizing entropy subject to total variation distance metric constraints, quantifying uncertainty of probability distributions by total variation distance metric, stochastic minimax control, and in many problems of information, decision theory, and minimax theory.

Place, publisher, year, edition, pages
2014. Vol. 59, no 9, 2353-2368 p.
Keyword [en]
Extremum probability measures, signed measures, total variation distance
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:kth:diva-155485DOI: 10.1109/TAC.2014.2321951ISI: 000342924100004ScopusID: 2-s2.0-84906538588OAI: diva2:762387

QC 20141111

Available from: 2014-11-11 Created: 2014-11-06 Last updated: 2014-11-11Bibliographically approved

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Charalambous, Themistoklis
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