Toric and non-toric Bayesian networks
Statistics Theory
2023-07-24 v2 Commutative Algebra
Statistics Theory
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.
Cite
@article{arxiv.2208.06294,
title = {Toric and non-toric Bayesian networks},
author = {Lisa Nicklasson},
journal= {arXiv preprint arXiv:2208.06294},
year = {2023}
}