A new characterization of discrete decomposable models

by   Eliana Duarte, et al.

Decomposable graphical models, also known as perfect DAG models, play a fundamental role in standard approaches to probabilistic inference via graph representations in modern machine learning and statistics. However, such models are limited by the assumption that the data-generating distribution does not entail strictly context-specific conditional independence relations. The family of staged tree models generalizes DAG models so as to accommodate context-specific knowledge. We provide a new characterization of perfect discrete DAG models in terms of their staged tree representations. This characterization identifies the family of balanced staged trees as the natural generalization of discrete decomposable models to the context-specific setting.


page 1

page 2

page 3

page 4


Representation and Learning of Context-Specific Causal Models with Observational and Interventional Data

We consider the problem of representation and learning of causal models ...

On perfectness in Gaussian graphical models

Knowing when a graphical model is perfect to a distribution is essential...

Algebraic geometry of discrete interventional models

We investigate the algebra and geometry of general interventions in disc...

A non-graphical representation of conditional independence via the neighbourhood lattice

We introduce and study the neighbourhood lattice decomposition of a dist...

Graphical Models with Attention for Context-Specific Independence and an Application to Perceptual Grouping

Discrete undirected graphical models, also known as Markov Random Fields...

A New Perspective on Learning Context-Specific Independence

Local structure such as context-specific independence (CSI) has received...

𝒮-adic characterization of minimal ternary dendric subshifts

Dendric subshifts are defined by combinatorial restrictions of the exten...