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The rectangular maximum agreement problem
Descriptive
TitleInfo
Title
The rectangular maximum agreement problem
SubTitle
applications and parallel solution
Name
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Kagawa
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Ai
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1986-
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Ai Kagawa
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author
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Eckstein
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Jonathan
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Jonathan Eckstein
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Advisory Committee
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chair
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Goldberg
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Noam
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Noam Goldberg
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Advisory Committee
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internal member
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Boros
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Endre
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Endre Boros
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Advisory Committee
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internal member
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Jeong
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Myong K.
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Myong K. Jeong
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Advisory Committee
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internal member
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BEN-ISRAEL
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ADI BEN-ISRAEL
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Advisory Committee
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Rutgers University
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degree grantor
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School of Graduate Studies
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Text
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theses
OriginInfo
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2018
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2018-10
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2018
Place
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xx
Language
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eng
Abstract
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A NP-hard rectangular maximum agreement (RMA) problem finds a “box” that best discriminates between two weighted datasets. We respectively describe a specialized parallel branch-and-bound method and a greedy heuristic to solve RMA exactly or approximately. Our computational results show that a new parallel branch-and-bound method can solve larger RMA problems exactly in less time than a previously implemented parallel branch-and-bound procedure and Gurobi, a mixed integer programming (MIP) solver.
We describe two applications of RMA: LPBoost-based two-class classification and a rule-enhanced penalized regression. The first classification application constructs a stronger classifier from a set of weighted voting classifiers by maximizing the margin between the two observation classes
and penalizing classification errors. The weighted voting classifiers are multidimensional ``box''-based rules. The second regression application formulates a L1-penalized regression model using multidimensional “box”-based rules as additional explanatory variables.
Due to exponentially large number of possible multidimensional rules, they are dynamically generated in both applications. In contrast to prior approaches to solve these problems, we draw heavily on
standard (but non-polynomial-time) mathematical programming techniques, enhanced by parallel computing. Our rule-adding procedure is based on the classical column generation method for high-dimensional linear programming. The pricing problem for our column generation procedure reduces to the RMA problem, and it is solved exactly or approximately. This method resembles boosting in machine learning. Furthermore, we propose a discretization method before solving RMA. It reduces the level of difficulty for RMA while still maintaining prediction or classification accuracy in the applications. The prediction accuracy of our models are tested by cross-validation. The resulting classification and regression methods are computation-intensive, but our computational tests suggest that they outperform prior methods at making accurate and stable predictions.
We describe two applications of RMA: LPBoost-based two-class classification and a rule-enhanced penalized regression. The first classification application constructs a stronger classifier from a set of weighted voting classifiers by maximizing the margin between the two observation classes
and penalizing classification errors. The weighted voting classifiers are multidimensional ``box''-based rules. The second regression application formulates a L1-penalized regression model using multidimensional “box”-based rules as additional explanatory variables.
Due to exponentially large number of possible multidimensional rules, they are dynamically generated in both applications. In contrast to prior approaches to solve these problems, we draw heavily on
standard (but non-polynomial-time) mathematical programming techniques, enhanced by parallel computing. Our rule-adding procedure is based on the classical column generation method for high-dimensional linear programming. The pricing problem for our column generation procedure reduces to the RMA problem, and it is solved exactly or approximately. This method resembles boosting in machine learning. Furthermore, we propose a discretization method before solving RMA. It reduces the level of difficulty for RMA while still maintaining prediction or classification accuracy in the applications. The prediction accuracy of our models are tested by cross-validation. The resulting classification and regression methods are computation-intensive, but our computational tests suggest that they outperform prior methods at making accurate and stable predictions.
Subject
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Topic
Operations Research
Subject
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Topic
Machine learning
Subject
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Topic
Rectangular maximum agreement
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Rutgers University Electronic Theses and Dissertations
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ETD_9185
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electronic resource
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application/pdf
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Extent
1 online resource (112 pages) : illustrations
Note
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Ph.D.
Note
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Includes bibliographical references
Note
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by Ai Kagawa
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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NjNbRU
Identifier
(type = doi)
doi:10.7282/t3-zb70-5663
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
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The author owns the copyright to this work.
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Name
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Kagawa
GivenName
Ai
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Type
Permission or license
DateTime
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2018-09-12 09:28:51
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Name
Ai Kagawa
Role
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Affiliation
Rutgers University. School of Graduate Studies
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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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2018-09-12T09:24:23
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2018-09-12T09:24:23
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