Toric and Non-toric Bayesian Networks

DOI10.1137/22m1515690arXiv2208.06294OpenAlexW4384933297MaRDI QIDQ6116681

Lisa Nicklasson

Publication date: 16 August 2023

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.06294

zbMATH Keywords

Bayesian networksalgebraic statisticstoric rings

Mathematics Subject Classification ID

Graphical methods in statistics (62A09) Commutative rings defined by binomial ideals, toric rings, etc. (13F65) Algebraic statistics (62R01) Theory of modules and ideals in commutative rings described by combinatorial properties (13C70)

Cites Work

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• Conditional independence and chain event graphs
• Markov bases for decomposable graphical models
• Gröbner bases and polyhedral geometry of reducible and cyclic models.
• Gröbner bases for staged trees
• Staged tree models with toric structure
• Equations defining probability tree models
• Algebraic geometry of Bayesian networks
• Conjunctive Bayesian networks
• Toric statistical models: parametric and binomial representations
• On the toric algebra of graphical models
• Algebraic Statistics
• Sagbi bases with applications to blow-up algebras.
• A new characterization of discrete decomposable graphical models

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