Algebraic Geometry of Bayesian Networks

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dc.contributor.authorGarcia-Puente, Luis Daviden
dc.contributor.committeechairLaubenbacher, Reinhard C.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.committeememberFarkas, Daniel R.en
dc.contributor.committeememberGreen, Edward L.en
dc.contributor.committeememberShimozono, Mark M.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2011-08-22T19:00:00Zen
dc.date.adate2004-04-19en
dc.date.available2011-08-22T19:00:00Zen
dc.date.issued2004-01-30en
dc.date.rdate2004-04-19en
dc.date.sdate2004-04-16en
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
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.otheretd-04162004-172816en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04162004-172816en
dc.identifier.urihttp://hdl.handle.net/10919/11133en
dc.publisherVirginia Techen
dc.relation.haspartthesis.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectstatistical modellingen
dc.subjectalgebraic geometryen
dc.subjectbayesian networksen
dc.subjectcomputational commutative algebraen
dc.subjectstatisticsen
dc.titleAlgebraic Geometry of Bayesian Networksen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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