Polyhedral aspects of maxoids

This repository contains a Julia package for working with conditional independence of max-linear Bayesian networks. It accompanies the paper Polyhedral aspects of maxoids (arxiv).

The conditional independence (CI) relation of a distribution in a max-linear Bayesian network depends on its weight matrix through the $C^\ast$-separation criterion. These CI models, which we call maxoids, are compositional graphoids which are in general not representable by Gaussian random variables. Every maxoid can be obtained from a transitively closed weighted DAG the stratification of generic weight matrices by their maxoids yields a polyhedral fan. This can be computed with this code. This connection to polyhedral geometry is results in an algorithm for solving the conditional independence implication problem for maxoids.