Vol. 12, No. 2, 2021

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Discrete max-linear Bayesian networks

Benjamin Hollering and Seth Sullivant

Vol. 12 (2021), No. 2, 213–225
DOI: 10.2140/astat.2021.12.213
Abstract

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.

Keywords
max-linear Bayesian network, conjunctive Bayesian network, toric ideal, tropical geometry
Mathematical Subject Classification
Primary: 13P25, 14M25
Milestones
Received: 12 February 2021
Revised: 8 July 2021
Accepted: 16 August 2021
Published: 13 December 2021
Authors
Benjamin Hollering
Deaprtment of Mathematics
North Carolina State University
Raleigh, NC
United States
Seth Sullivant
Deaprtment of Mathematics
North Carolina State University
Raleigh, NC
United States