Type of Document	Dissertation
Author	Garcia-Puente, Luis David
Author's Email Address	lgarcia@math.vt.edu
URN	etd-04162004-172816
Title	Algebraic Geometry of Bayesian Networks
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Laubenbacher, Reinhard C. Committee Chair Brown, Ezra A. Committee Member Farkas, Daniel R. Committee Member Green, Edward L. Committee Member Shimozono, Mark M. Committee Member
Keywords	statistical modelling algebraic geometry bayesian networks computational commutative algebra statistics
Date of Defense	2004-04-01
Availability	unrestricted
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.
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