Conditional independence in max-linear Bayesian networks

Research output: Contribution to journalJournal articlepeer-review

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Conditional independence in max-linear Bayesian networks. / Amendola, Carlos; Kluppelberg, Claudia; Lauritzen, Steffen; Tran, Ngoc.

In: Annals of Applied Probability, Vol. 32, No. 1, 2022, p. 1-45.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Amendola, C, Kluppelberg, C, Lauritzen, S & Tran, N 2022, 'Conditional independence in max-linear Bayesian networks', Annals of Applied Probability, vol. 32, no. 1, pp. 1-45. https://doi.org/10.1214/21-AAP1670

APA

Amendola, C., Kluppelberg, C., Lauritzen, S., & Tran, N. (2022). Conditional independence in max-linear Bayesian networks. Annals of Applied Probability, 32(1), 1-45. https://doi.org/10.1214/21-AAP1670

Vancouver

Amendola C, Kluppelberg C, Lauritzen S, Tran N. Conditional independence in max-linear Bayesian networks. Annals of Applied Probability. 2022;32(1):1-45. https://doi.org/10.1214/21-AAP1670

Author

Amendola, Carlos ; Kluppelberg, Claudia ; Lauritzen, Steffen ; Tran, Ngoc. / Conditional independence in max-linear Bayesian networks. In: Annals of Applied Probability. 2022 ; Vol. 32, No. 1. pp. 1-45.

Bibtex

@article{aebcf1f4ba49426fb9c1dcaa59212685,
title = "Conditional independence in max-linear Bayesian networks",
abstract = "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.",
author = "Carlos Amendola and Claudia Kluppelberg and Steffen Lauritzen and Ngoc Tran",
year = "2022",
doi = "10.1214/21-AAP1670",
language = "English",
volume = "32",
pages = "1--45",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "1",

}

RIS

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