Tropical combinatorics of max-linear Bayesian networks

Tropical combinatorics of max-linear Bayesian networks

A polytrope is a tropical polyhedron that is also classically convex. We study the tropical combinatorial types of polytropes associated to weighted directed acyclic graphs (DAGs). This family of polytropes arises in algebraic statistics when describing the model class of max-linear Bayesian network...

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Bibliographic Details
Main Authors: Améndola, Carlos, Ferry, Kamillo
Format: Journal Article
Language:English
Published: 15-11-2024
Subjects:
Mathematics - Algebraic Geometry
Mathematics - Combinatorics
Mathematics - Statistics Theory
Statistics - Theory
Online Access:Get full text
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Summary:A polytrope is a tropical polyhedron that is also classically convex. We study the tropical combinatorial types of polytropes associated to weighted directed acyclic graphs (DAGs). This family of polytropes arises in algebraic statistics when describing the model class of max-linear Bayesian networks. We show how the edge weights of a network directly relate to the facet structure of the corresponding polytrope. We also give a classification of polytropes from weighted DAGs at different levels of equivalence. These results give insight on the statistical problem of identifiability for a max-linear Bayesian network.
DOI:10.48550/arxiv.2411.10394