Titre :

Limits of Multi-relational Graphs

Auteur(s) :

Alvarado, Juan [Auteur]
Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]
Wang, Yuyi [Auteur]
Department of Computer Science [ETH Zürich] [D-INFK]
Ramon, Jan [Auteur]
Machine Learning in Information Networks [MAGNET]

Titre de la revue :

Machine Learning

Pagination :

177–216

Éditeur :

Springer Verlag

Date de publication :

2022-11

ISSN :

0885-6125

Mot(s)-clé(s) en anglais :

Large multigraph
Graphon Theory
Markov Logic Network
Large Deviation Principle

Discipline(s) HAL :

Informatique [cs]/Intelligence artificielle [cs.AI]
Mathématiques [math]/Statistiques [math.ST]
Physique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an]
Statistiques [stat]/Machine Learning [stat.ML]

Résumé en anglais : [en]

Graphons are limits of large graphs. Motivated by a theoretical problem from statistical relational learning, we develop a generalization of basic results from graphon theory into the "multi-relational" setting. We show ...
Lire la suite >Graphons are limits of large graphs. Motivated by a theoretical problem from statistical relational learning, we develop a generalization of basic results from graphon theory into the "multi-relational" setting. We show that their multi-relational counterparts, which we call multi-relational graphons, are analogically limits of large multi-relational graphs. We extend the cutdistance topology for graphons to multi-relational graphons and prove its compactness and the density of multi-relational graphs in this topology. In turn, compactness enables to prove the large deviation principle for Multi-Relational Graphs (LDP) which enables to prove the most typical random graphs constrained by marginal statistics converge asymptotically to constrained multirelational graphons with maximum entropy. We show the equivalence between a restricted version of Markov Logic Network and Multi-Relational Graphons with maximum entropy.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL