论文标题
可分解的特定于上下文模型
Decomposable context-specific models
论文作者
论文摘要
我们介绍了一个离散背景特定模型的家族，我们称之为分解。我们从分阶段的树模型的子类中构建了这个家庭。我们给出了在可分解的特定上下文特定模型中存在的所有特定于上下文独立关系的代数和组合表征，该模型产生了马尔可夫的基础。我们证明，适用于特定于上下文模型的图形表示的道德化操作不会影响隐含的独立关系，因此确认这些模型是由有限的可分解图形模型的有限收集来描述的。更普遍地，我们确定可分解的上下文特定模型的几种代数，组合和几何特性将可分解图形模型的模型推广到上下文特定的设置。
We introduce a family of discrete context-specific models, which we call decomposable. We construct this family from the subclass of staged tree models known as CStree models. We give an algebraic and combinatorial characterization of all context-specific independence relations that hold in a decomposable context-specific model, which yields a Markov basis. We prove that the moralization operation applied to the graphical representation of a context-specific model does not affect the implied independence relations, thus affirming that these models are algebraically described by a finite collection of decomposable graphical models. More generally, we establish that several algebraic, combinatorial, and geometric properties of decomposable context-specific models generalize those of decomposable graphical models to the context-specific setting.
