Tropical combinatorics of Max-Linear Bayesian Networks

Max-linear Bayesian networks (MLBNs) are recursive max-linear structural equation model represented by an edge weighted directed acyclic graph (DAG). Their recursive structural equations are given over the max-times semiring which indicates a deep connection to tropical geometry. The solution to the recursive equations imply that the observational data from an MLBN lies inside a polytrope, which is a tropical polyhedron that is also classically convex. Thus, we study the tropical combinatorial types of polytropes associated to MLBNs by enumerating triangulations of certain point configurations. We report on the number of combinatorial types for n up to 6 and also touch upon the consequences of our classification for the identifiability of weights.

This is based on joint work with Carlos Améndola.