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.
翻译:我们引入了一套离散的因地制宜的模式,我们称之为可分解的。我们从称为CStree模型的分阶段树型模式子类中构建了这个家庭。我们用可分解的因地制宜的模型对所有因地制宜的独立关系进行代数和组合式定性,得出了Markov的根据。我们证明,适用于因地制宜模式图形表达的道德化操作并不影响隐含的独立关系,从而肯定这些模型是用有限的可分解的图形模型来代数描述的。更一般地说,我们确定若干可分解的因地制具体环境模型的代数、组合和几何特性,将可分解的因地制宜的图形模型与因地制宜地制宜。