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Date
2023-01Type
- Journal Article
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 cut-distance 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 multi-relational graphons with maximum entropy. We show the equivalence between a restricted version of Markov Logic Network and Multi-Relational Graphons with maximum entropy. Show more
Publication status
publishedExternal links
Journal / series
Machine LearningVolume
Pages / Article No.
Publisher
SpringerSubject
Large multigraph; Graphon theory; Markov logic network; Large deviation principleMore
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