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Journal Articles Machine Learning Year : 2022

Limits of Multi-relational Graphs

Abstract

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.
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Dates and versions

hal-03881631 , version 1 (01-12-2022)

Identifiers

  • HAL Id : hal-03881631 , version 1

Cite

Juan Aurelio Alvarado, Yuyi Wang, Jan Ramon. Limits of Multi-relational Graphs. Machine Learning, 2022. ⟨hal-03881631⟩
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