Entropic Projections and Dominating Points

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 deviat...

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Published inProbability and statistics Vol. 14; pp. 343 - 381
Main Author Léonard, Christian
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.01.2010
Subjects
46N10
60F10
60F99
60G57
Applied mathematics
Conditional laws of large numbers
Convex analysis
convex optimization
dominating points
entropic projections
Entropy
Functional Analysis
Information theory
Inverse problems
large deviations
Mathematical analysis
Mathematics
Numbers
Optimization
Orlicz spaces
Probability
random measures
Random variables
Statistical physics
Studies
large deviations
random measures
entropy
dominating points
Conditional laws of large numbers
convex optimization
entropic projections
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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.
AbstractList 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.
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. [PUBLICATION ABSTRACT]
Generalized 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 their existence. Representations of the generalized entropic projections are obtained: they are the ``measure component" of some extended entropy minimization problem.
Author Léonard, Christian
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  organization: Modal-X, Université Paris Ouest, Bât. G, 200 av. de la République, 92000 Nanterre, France; leonard@u-paris10.fr
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Keywords large deviations
random measures
entropy
dominating points
Conditional laws of large numbers
convex optimization
entropic projections
Language English
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Snippet Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many...
Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear...
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SubjectTerms 46N10
60F10
60F99
60G57
Applied mathematics
Conditional laws of large numbers
Convex analysis
convex optimization
dominating points
entropic projections
Entropy
Functional Analysis
Information theory
Inverse problems
large deviations
Mathematical analysis
Mathematics
Numbers
Optimization
Orlicz spaces
Probability
random measures
Random variables
Statistical physics
Studies
Title Entropic Projections and Dominating Points
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