Conditional independence in max-linear Bayesian networks
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Conditional independence in max-linear Bayesian networks. / Amendola, Carlos; Kluppelberg, Claudia; Lauritzen, Steffen; Tran, Ngoc.
I: Annals of Applied Probability, Bind 32, Nr. 1, 2022, s. 1-45.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Conditional independence in max-linear Bayesian networks
AU - Amendola, Carlos
AU - Kluppelberg, Claudia
AU - Lauritzen, Steffen
AU - Tran, Ngoc
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
U2 - 10.1214/21-AAP1670
DO - 10.1214/21-AAP1670
M3 - Journal article
VL - 32
SP - 1
EP - 45
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 1
ER -
ID: 298378459