Decomposable context-specific models. (English) Zbl 07871665
Summary: 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 a directed version of 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.
MSC:
| 62R01 | Algebraic statistics |
| 62A09 | Graphical methods in statistics |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 13P25 | Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) |
Keywords:
decomposable models; context-specific independence; Bayesian network; directed acyclic graph; toric ideal; algebraic statistics; probability treesReferences:
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