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Marginal Likelihood Integrals for Mixtures of Independence Models.

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Title: Marginal Likelihood Integrals for Mixtures of Independence Models.
Authors: Shaowei Lin1 SHAOWEI@MATH.BERKELEY.EDU, Sturmfels, Bernd1, Zhiqiang Xu2 XUZQ@LSEC.CC.AC.CN
Source: Journal of Machine Learning Research. 7/1/2009, Vol. 10 Issue 7, p1611-1631. 21p. 2 Diagrams, 1 Graph.
Subjects: Integrals, Algebraic independence, Mathematical models, Algorithms, Varieties (Universal algebra), Probability theory, Bayesian analysis
Abstract: Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors and Dirichlet priors. The underlying statistical models are mixtures of independent distributions, or, in geometric language, secant varieties of Segre-Veronese varieties. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Machine Learning Research is the property of Microtome Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 47676593
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Marginal Likelihood Integrals for Mixtures of Independence Models.
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  Data: <searchLink fieldCode="AR" term="%22Shaowei+Lin%22">Shaowei Lin</searchLink><relatesTo>1</relatesTo><i> SHAOWEI@MATH.BERKELEY.EDU</i><br /><searchLink fieldCode="AR" term="%22Sturmfels%2C+Bernd%22">Sturmfels, Bernd</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Zhiqiang+Xu%22">Zhiqiang Xu</searchLink><relatesTo>2</relatesTo><i> XUZQ@LSEC.CC.AC.CN</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Machine+Learning+Research%22">Journal of Machine Learning Research</searchLink>. 7/1/2009, Vol. 10 Issue 7, p1611-1631. 21p. 2 Diagrams, 1 Graph.
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  Data: <searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+independence%22">Algebraic independence</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Varieties+%28Universal+algebra%29%22">Varieties (Universal algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink>
– Name: Abstract
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  Data: Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors and Dirichlet priors. The underlying statistical models are mixtures of independent distributions, or, in geometric language, secant varieties of Segre-Veronese varieties. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Machine Learning Research is the property of Microtome Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 21
        StartPage: 1611
    Subjects:
      – SubjectFull: Integrals
        Type: general
      – SubjectFull: Algebraic independence
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Varieties (Universal algebra)
        Type: general
      – SubjectFull: Probability theory
        Type: general
      – SubjectFull: Bayesian analysis
        Type: general
    Titles:
      – TitleFull: Marginal Likelihood Integrals for Mixtures of Independence Models.
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          Name:
            NameFull: Shaowei Lin
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            NameFull: Sturmfels, Bernd
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            NameFull: Zhiqiang Xu
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            – D: 01
              M: 07
              Text: 7/1/2009
              Type: published
              Y: 2009
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              Value: 10
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