Selfadhesivity in Gaussian conditional independence structures
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Submission date: 17. May. 2022
MSC-Numbers: 62R01, 62B10, 15A29, 05B20
Keywords and phrases: selfadhesivity, adhesive extension, positive definite matrix, Conditional Independence, structural semigraphoid, orientable gaussoid
Link to arXiv: See the arXiv entry of this preprint.
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.