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Algebraic geometry of Bayesian networks. (English) Zbl 1126.68102
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:
68W30Symbolic computation and algebraic computation
68T05Learning and adaptive systems
13P10Gröbner bases; other bases for ideals and modules
14N05Projective techniques (algebraic geometry)
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