Markov Equivalence of MaxLinear Bayesian Networks
Abstract
Maxlinear Bayesian networks have emerged as highly applicable models for causal inference via extreme value data. However, conditional independence (CI) for maxlinear 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 maxlinear 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.08305
 Bibcode:
 2021arXiv210608305A
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 62H22;
 14T90;
 62G32;
 62R01
 EPrint:
 19 pages, 5 figures, accepted for the 37th conference on Uncertainty in Artificial Intelligence (UAI 2021)