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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:

68W30 Symbolic computation and algebraic computation
68T05 Learning and adaptive systems in artificial intelligence
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14N05 Projective techniques in algebraic geometry

Software:

Macaulay2; SINGULAR
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Full Text: DOI arXiv

References:

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