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Zbl 1126.68102
Garcia, Luis David; Stillman, Michael; Sturmfels, Bernd
Algebraic geometry of Bayesian networks. (English)
[J] J. Symb. Comput. 39, No. 3-4, 331-355 (2005). ISSN 0747-7171

Summary: We study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties.

MSC 2000:: *68W30 Symbolic computation and algebraic computation
68T05 Learning and adaptive systems
13P10 Polynomial ideals, Groebner bases
14N05 Projective techniques (classical algebraic geometry)

Keywords: algebraic statistics; Bayesian networks; independence models; polynomial ideals; decomposition; secant varieties; Segre varieties

Cited in: Zbl 1137.14038 Zbl 1131.92046 Zbl 1130.14041

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