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Discrete max-linear
Bayesian networks
Benjamin Hollering and Seth Sullivant |
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Vol. 12 (2021), No. 2, 213–225
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DOI: 10.2140/astat.2021.12.213
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Abstract |
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Discrete max-linear Bayesian networks are directed graphical models specified by the same recursive structural equations as max-linear models but with discrete innovations. When all of the random variables in the model are binary, these models are isomorphic to the conjunctive Bayesian network (CBN) models of Beerenwinkel, Eriksson, and Sturmfels. Many of the techniques used to study CBN models can be extended to discrete max-linear models and similar results can be obtained. In particular, we extend the fact that CBN models are toric varieties after linear change of coordinates to all discrete max-linear models. |
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Keywords
max-linear Bayesian network, conjunctive Bayesian network,
toric ideal, tropical geometry
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Mathematical Subject Classification
Primary: 13P25, 14M25
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Milestones
Received: 12 February 2021
Revised: 8 July 2021
Accepted: 16 August 2021
Published: 13 December 2021
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Authors |
| Benjamin Hollering | |
| Deaprtment of Mathematics North Carolina State University Raleigh, NC United States |
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| Seth Sullivant | |
| Deaprtment of Mathematics North Carolina State University Raleigh, NC United States |
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