论文标题
福利和非贝叶斯网络
Toric and non-toric Bayesian networks
论文作者
论文摘要
在本文中，我们从交换代数的角度研究贝叶斯网络。我们表征了一类感谢您的贝叶斯网，并提供了贝叶斯网的第一个例子，该贝叶斯网被证明是在变量的任何线性变化下被证明是无效的。关于福利贝叶斯网的类别，我们研究了它们的二次关系，并证明了加西亚，斯蒂尔曼和斯特尔姆菲尔斯的猜想。此外，我们在所有关系都是二次的何时给基础的定向无环图提供了必要的条件。
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.
