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Extracting sparse signals from high-dimensional data
Descriptive
TitleInfo
Title
Extracting sparse signals from high-dimensional data
SubTitle
a statistical mechanics approach
Name
(type = personal)
NamePart
(type = family)
Ramezanali
NamePart
(type = given)
Mohammad
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Mohammad Ramezanali
Role
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author
Name
(type = personal)
NamePart
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Sengupta
NamePart
(type = given)
Anirvan M
DisplayForm
Anirvan M Sengupta
Affiliation
Advisory Committee
Role
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chair
Name
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NamePart
Rutgers University
Role
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degree grantor
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NamePart
Graduate School - New Brunswick
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school
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Text
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theses
OriginInfo
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2015
DateOther
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(type = degree)
2015-10
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2015
Place
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xx
Language
LanguageTerm
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(type = code)
eng
Abstract
(type = abstract)
Sparse reconstruction algorithms aim to retrieve high-dimensional sparse signals from a limited amount of measurements under suitable conditions. As the number of variables go to infinity, these algorithms exhibit sharp phase transition boundaries where the sparse retrieval breaks down. Several sparse reconstruction algorithms are formulated as optimization problems. Few of the prominent ones among these have been analyzed in the literature by statistical mechanical methods. The function to be optimized plays the role of energy. The treatment involves finite temperature replica mean-field theory followed by the zero temperature limit. Although this approach has been successful in reproducing the algorithmic phase transition boundaries, the replica trick and the non-trivial zero temperature limit obscure the underlying reasons for the failure of the algorithms. In this thesis, we employ the ``cavity method" to give an alternative derivation of the phase transition boundaries, working directly in the zero-temperature limit. This approach provides insight into the origin of the different terms in the mean field self-consistency equations. The cavity method naturally generates a local susceptibility which leads to an identity that clearly indicates the existence of two phases. The identity also gives us a novel route to the known parametric expressions for the phase boundary of the Basis Pursuit algorithm and to the new ones for the Elastic Net. These transitions being continuous (second order), we explore the scaling laws and critical exponents that are uniquely determined by the nature of the distribution of the density of the nonzero components of the sparse signal. Not only is the phase boundary of the Elastic Net different from that of the Basis Pursuit, we show that the critical behavior of the two algorithms are from different universality classes.
Subject
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Topic
Physics and Astronomy
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
Identifier
ETD_6673
PhysicalDescription
Form
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electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (xii, 89 p. : ill.)
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Subject
(authority = ETD-LCSH)
Topic
Statistical mechanics
Note
(type = statement of responsibility)
by Mohammad Ramezanali
RelatedItem
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
Location
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3736SWR
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Ramezanali
GivenName
Mohammad
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(point = start)
2015-08-26 15:38:30
AssociatedEntity
Name
Mohammad Ramezanali
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical
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ETD
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windows xp
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