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：本文引入了一类离散的上下文特定模型，我们将其称为可分解模型。我们从已知的分阶段树模型子类CStree模型出发构建该族模型。我们给出了可分解上下文特定模型中所有成立的上下文特定独立关系的代数与组合刻画，并由此得到一组马尔可夫基。我们证明了在上下文特定模型的图表示上应用道德化操作不会影响其隐含的独立关系，从而证实这些模型可由有限个可分解图模型通过代数方式描述。更一般地，我们建立了可分解上下文特定模型在代数、组合与几何性质上的若干推广——将可分解图模型的相应性质推广至上下文特定场景。