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dc.contributor.authorGarcia-Puente, Luis Daviden_US
dc.date.accessioned2011-08-22T19:00:00Z
dc.date.available2011-08-22T19:00:00Z
dc.date.issued2004-01-30en_US
dc.identifier.otheretd-04162004-172816en_US
dc.identifier.urihttp://hdl.handle.net/10919/11133
dc.description.abstractWe develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.relation.haspartthesis.pdfen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectstatistical modellingen_US
dc.subjectalgebraic geometryen_US
dc.subjectbayesian networksen_US
dc.subjectcomputational commutative algebraen_US
dc.subjectstatisticsen_US
dc.titleAlgebraic Geometry of Bayesian Networksen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairLaubenbacher, Reinhard C.en_US
dc.contributor.committeememberBrown, Ezra A.en_US
dc.contributor.committeememberFarkas, Daniel R.en_US
dc.contributor.committeememberGreen, Edward L.en_US
dc.contributor.committeememberShimozono, Mark M.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04162004-172816en_US
dc.date.sdate2004-04-16en_US
dc.date.rdate2004-04-19
dc.date.adate2004-04-19en_US


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