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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
19/2022

Selfadhesivity in Gaussian conditional independence structures

Tobias Boege

Abstract

Selfadhesivity is a property of entropic polymatroids which can be formulated as gluability conditions of the polymatroid to an identical copy of itself along arbitrary restrictions and such that the two pieces are independent given the common restriction.

We show that positive definite matrices satisfy this condition as well and examine consequences for Gaussian conditional independence structures. New axioms of Gaussian CI are obtained by applying selfadhesivity to the previously known axioms of structural semigraphoids and orientable gaussoids.

Received:
17.05.22
Published:
17.05.22
MSC Codes:
62R01, 62B10, 15A29, 05B20
Keywords:
selfadhesivity, adhesive extension, positive definite matrix, Conditional Independence, structural semigraphoid, orientable gaussoid

Related publications

inJournal
2023 Journal Open Access
Tobias Boege

Selfadhesivity in Gaussian conditional independence structures

In: International journal of approximate reasoning, 163 (2023), p. 109027