Algebraic geometry of discrete interventional models

Duarte, Eliana; Solus, Liam

doi:10.48550/arxiv.2012.03593

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…A result similar in spirit to Proposition 2 was derived in Duarte and Solus (2020) formalizing the equivalence between decomposable BNs and balanced staged trees, which are characterized by a polynomial condition based on interpolating polynomials (Görgen et al, 2015), holding for all simple staged trees. Görgen et al (2020) demonstrated that balanced staged trees, and thus also simple ones, are regular exponential families.…”

Section: Simple Staged Treesmentioning

confidence: 83%

Structural Learning of Simple Staged Trees

Leonelli¹,

Varando²

2022

Preprint

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Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents nonsymmetric conditional independences via vertex coloring. However, since they are based on a tree representation of the sample space, the underlying graph becomes cluttered and difficult to visualize as the number of variables increases. Here we introduce the first structural learning algorithms for the class of simple staged trees, entertaining a compact coalescence of the underlying tree from which non-symmetric independences can be easily read. We show that data-learned simple staged trees often outperform Bayesian networks in model fit and illustrate how the coalesced graph is used to identify non-symmetric conditional independences.

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Section: Simple Staged Treesmentioning

confidence: 83%

Structural Learning of Simple Staged Trees

Leonelli¹,

Varando²

2022

Preprint

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“…As demonstrated by Smith and Anderson (2008) and Duarte and Solus (2020), every BN can be represented as a staged tree. However, the class of staged tree models is much more general and can represent not only symmetric, but also context-specific, partial and local independences, using the terminology of Pensar et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Staged trees and asymmetry-labeled DAGs

Varando¹,

Carli²,

Leonelli³

2021

Preprint

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Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. They can be seen as a special case of the much more general class of models called staged trees, which can represent any type of non-symmetric conditional independence. Here we formalize the relationship between these two models and introduce a minimal Bayesian network representation of the staged tree, which can be used to read conditional independences in an intutitive way. Furthermore, we define a new labeled graph, termed asymmetry-labeled directed acyclic graph, whose edges are labeled to denote the type of dependence existing between any two random variables. Various datasets are used to illustrate the methodology, highlighting the need to construct models which more flexibly encode and represent non-symmetric structures.

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Algebraic geometry of discrete interventional models

Cited by 2 publications

References 22 publications

Structural Learning of Simple Staged Trees

Structural Learning of Simple Staged Trees

Staged trees and asymmetry-labeled DAGs

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