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arXiv · 2208.06294

Toric and non-toric Bayesian networks

Lisa Nicklasson
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Abstract

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.

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Lisa Nicklasson. 2022-08-12. Toric and non-toric Bayesian networks. https://doi.org/10.1137/22m1515690

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