环向和非环向贝叶斯网络

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2022-08-12 DOI:10.1137/22M1515690

Lisa Nicklasson

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引用次数: 1

摘要

本文从交换代数的角度研究贝叶斯网络。刻画了一类环向贝叶斯网，并给出了在任意变量线性变化条件下证明非环向贝叶斯网的第一个例子。关于环面贝叶斯网类，我们研究了它们的二次关系，并证明了Garcia、Stillman和Sturmfels为该类提出的一个猜想。此外，我们还给出了有向无环图下所有关系都是二次关系的一个必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Toric and Non-toric Bayesian Networks

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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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量