Markov Equivalence of Max-Linear Bayesian Networks

Abstract

Max-linear Bayesian networks have emerged as highly applicable models for causal inference via extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian Bayesian networks. We establish the parallel between the two theories via tropicalization, and establish the surprising result that the Markov equivalence classes for max-linear Bayesian networks coincide with the ones obtained by regular CI. Our paper opens up many problems at the intersection of extreme value statistics, causal inference and tropical geometry.