CONDITIONAL INDEPENDENCE IN MAX-LINEAR BAYESIAN NETWORKS
成果类型：
Article
署名作者：
Amendola, Carlos; Klueppelberg, Claudia; Lauritzen, Steffen; Tran, Ngoc M.
署名单位：
Technical University of Munich; University of Copenhagen; University of Texas System; University of Texas Austin
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/21-AAP1670
发表日期：
2022
页码：
1-45
关键词：
摘要：
Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for Bayesian networks are far from exhausting valid conditional independence statements. We use tropical linear algebra to derive a compact representation of the conditional distribution given a partial observation, and exploit this to obtain a complete description of all conditional independence relations. In the context-specific case, where conditional independence is queried relative to a specific value of the conditioning variables, we introduce the notion of a source DAG to disclose the valid conditional independence relations. In the context-free case, we characterize conditional independence through a modified separation concept,( )(*)-separation, combined with a tropical eigenvalue condition. We also introduce the notion of an impact graph, which describes how extreme events spread deterministically through the network and we give a complete characterization of such impact graphs. Our analysis opens up several interesting questions concerning conditional independence and tropical geometry.