Entropic Projections and Dominating Points

Christian Léonard

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 343-381
  • ISSN: 1292-8100

Abstract

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Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for the existence of entropic projections, generalized entropic projections and dominating points. Representations of the generalized entropic projections are obtained. It is shown that they are the “measure component" of the solutions to some extended entropy minimization problem. This approach leads to new results and offers a unifying point of view. It also permits to extend previous results on the subject by removing unnecessary topological restrictions. As a by-product, new proofs of already known results are provided.

How to cite

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Léonard, Christian. "Entropic Projections and Dominating Points." ESAIM: Probability and Statistics 14 (2010): 343-381. <http://eudml.org/doc/250830>.

@article{Léonard2010,
abstract = { Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for the existence of entropic projections, generalized entropic projections and dominating points. Representations of the generalized entropic projections are obtained. It is shown that they are the “measure component" of the solutions to some extended entropy minimization problem. This approach leads to new results and offers a unifying point of view. It also permits to extend previous results on the subject by removing unnecessary topological restrictions. As a by-product, new proofs of already known results are provided. },
author = {Léonard, Christian},
journal = {ESAIM: Probability and Statistics},
keywords = {Conditional laws of large numbers; random measures; large deviations; entropy; convex optimization; entropic projections; dominating points; Orlicz spaces; laws of large numbers; large deviations},
language = {eng},
month = {12},
pages = {343-381},
publisher = {EDP Sciences},
title = {Entropic Projections and Dominating Points},
url = {http://eudml.org/doc/250830},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Léonard, Christian
TI - Entropic Projections and Dominating Points
JO - ESAIM: Probability and Statistics
DA - 2010/12//
PB - EDP Sciences
VL - 14
SP - 343
EP - 381
AB - Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for the existence of entropic projections, generalized entropic projections and dominating points. Representations of the generalized entropic projections are obtained. It is shown that they are the “measure component" of the solutions to some extended entropy minimization problem. This approach leads to new results and offers a unifying point of view. It also permits to extend previous results on the subject by removing unnecessary topological restrictions. As a by-product, new proofs of already known results are provided.
LA - eng
KW - Conditional laws of large numbers; random measures; large deviations; entropy; convex optimization; entropic projections; dominating points; Orlicz spaces; laws of large numbers; large deviations
UR - http://eudml.org/doc/250830
ER -

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