Title page for ETD etd-04162004-172816


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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