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A linear programming model for sequential testing
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A linear programming model for sequential testing
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Fedzhora
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Liliya
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Liliya Fedzhora
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Andras
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Andras Prekopa
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Boros
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Endre Boros
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Vladimir
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Vladimir Gurvich
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Kantor
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Paul
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Paul Kantor
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Advisory Committee
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Bela Vizvari
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Rutgers University
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Graduate School - New Brunswick
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theses
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2008
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2008-10
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English
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electronic
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viii, 89 pages
Abstract
In this study, a linear programming model is formulated that finds an optimal strategy for many decision-making problems that typically arise in homeland security, banking, medicine, and engineering. We consider the problem of deploying a set of tests most effectively when the goal is to detect as many as possible "bad" objects among the vast majority of "good" ones, for example, in searching for contraband. The study assumes that functional dependency between test results and object type is unknown. The model finds an optimal testing strategy in the form of a decision tree that minimizes the expected cost given a detection rate or maximizes the detection rate given the budget. The mathematical basis for the model is a polyhedral description of all decision trees in higher dimensional space.
Decision trees are widely used in data mining and machine learning. A notion of VCdimension is used to evaluate the bounds of the sample size required for the learning model. For some classes of Boolean functions VC-dimension is already known, for example, for monomials and threshold functions. In Chapter 10, the VC-dimension of Horn functions is derived, and also the VC-dimension of a more general class of k-quasi-Horn functions. In Chapter 11 we state and prove a criterion for k-quasi-Horn functions that generalizes McKinsey's theorem. Also, necessary and sufficient conditions for function to be bidual k-quasi-Horn are stated and proved.
Decision trees are widely used in data mining and machine learning. A notion of VCdimension is used to evaluate the bounds of the sample size required for the learning model. For some classes of Boolean functions VC-dimension is already known, for example, for monomials and threshold functions. In Chapter 10, the VC-dimension of Horn functions is derived, and also the VC-dimension of a more general class of k-quasi-Horn functions. In Chapter 11 we state and prove a criterion for k-quasi-Horn functions that generalizes McKinsey's theorem. Also, necessary and sufficient conditions for function to be bidual k-quasi-Horn are stated and proved.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 83-88).
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Operations Research
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Decision making
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Data mining
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Topic
Sequential analysis
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17466
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doi:10.7282/T3Z038HZ
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ETD doctoral
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Liliya Fedzhora
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Rutgers University. Graduate School - New Brunswick
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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.
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