Type of Document Dissertation Author Garcia-Puente, Luis David Author's Email Address email@example.com 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
Date of Defense 2004-04-01 Availability unrestricted 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.
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