Self-adhesivity in lattices of abstract conditional independence models

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F25%3A00599870" target="_blank" >RIV/67985556:_____/25:00599870 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0166218X2400430X?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0166218X2400430X?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.dam.2024.10.006" target="_blank" >10.1016/j.dam.2024.10.006</a>

Result language

angličtina

Original language name

Self-adhesivity in lattices of abstract conditional independence models

Original language description

We introduce an algebraic concept of the frame for abstract conditional independence (CI) models, together with basic operations with respect to which such a frame should be closed: copying and marginalization. Three standard examples of such frames are (discrete) probabilistic CI structures, semi-graphoids and structural semi-graphoids. We concentrate on those frames which are closed under the operation of set-theoretical intersection because, for these, the respective families of CI models are lattices. This allows one to apply the results from lattice theory and formal concept analysis to describe such families in terms of implications among CI statements.nnThe central concept of this paper is that of self-adhesivity defined in algebraic terms, which is a combinatorial reflection of the self-adhesivity concept studied earlier in context of polymatroids and information theory. The generalization also leads to a self-adhesivity operator defined on the meta-level of CI frames. We answer some of the questions related to this approach and raise other open questions.nnThe core of the paper is in computations. The combinatorial approach to computation might overcome some memory and space limitation of software packages based on polyhedral geometry, in particular, if SAT solvers are utilized. We characterize some basic CI families over 4 variables in terms of canonical implications among CI statements. We apply our method in information-theoretical context to the task of entropic region demarcation over 5 variables.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Discrete Applied Mathematics

ISSN

0166-218X

e-ISSN

1872-6771

Volume of the periodical

361

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

30

Pages from-to

196-225

UT code for WoS article

001344013900001

EID of the result in the Scopus database

2-s2.0-85207029715