Toric and non-toric Bayesian networks

Lisa Nicklasson

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Toric and non-toric Bayesian networks

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arxiv 2208.06294 v2 pith:XAF4VUQ2 submitted 2022-08-12 math.ST math.ACstat.TH

Toric and non-toric Bayesian networks

Lisa Nicklasson This is my paper

classification math.ST math.ACstat.TH

keywords bayesianclasstoricnetsnetworksnon-toricquadraticrelations

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In this paper we study Bayesian networks from a commutative algebra perspective. We characterize a class of toric Bayesian nets, and provide the first example of a Bayesian net which is proved non-toric under any linear change of variables. Concerning the class of toric Bayesian nets, we study their quadratic relations and prove a conjecture by Garcia, Stillman, and Sturmfels for this class. In addition, we give a necessary condition on the underlying directed acyclic graph for when all relations are quadratic.

Toric and non-toric Bayesian networks

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