Algebraic Geometry of Bayesian Networks Export

@phdthesis{citeulike:3875368, abstract = {We 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.}, author = {Garcia-Puente, Luis D.}, citeulike-article-id = {3875368}, citeulike-linkout-0 = {http://scholar.lib.vt.edu/theses/available/etd-04162004-172816/unrestricted/thesis.pdf}, keywords = {algebraic-geometry, baysian-network}, posted-at = {2009-01-12 10:23:43}, priority = {2}, title = {Algebraic Geometry of Bayesian Networks}, url = {http://scholar.lib.vt.edu/theses/available/etd-04162004-172816/unrestricted/thesis.pdf} }

TY - THES ID - citeulike:3875368 L3 - citeulike-article-id:3875368 N2 - We 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. TI - Algebraic Geometry of Bayesian Networks KW - algebraic-geometry KW - baysian-network AU - Garcia-Puente, Luis UR - http://scholar.lib.vt.edu/theses/available/etd-04162004-172816/unrestricted/thesis.pdf ER -