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-relationa...
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| Autor*in: |
Alvarado, Juan [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Machine learning - Springer US, 1986, 112(2022), 1 vom: 13. Dez., Seite 177-216 |
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| Übergeordnetes Werk: |
volume:112 ; year:2022 ; number:1 ; day:13 ; month:12 ; pages:177-216 |
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| DOI / URN: |
10.1007/s10994-022-06281-x |
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| 520 | |a 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. | ||
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| 700 | 1 | |a Wang, Yuyi |4 aut | |
| 700 | 1 | |a Ramon, Jan |4 aut | |
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10.1007/s10994-022-06281-x doi (DE-627)OLC2080325957 (DE-He213)s10994-022-06281-x-p DE-627 ger DE-627 rakwb eng 150 004 VZ Alvarado, Juan verfasserin (orcid)0000-0002-9794-3675 aut Limits of multi-relational graphs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 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. Large multigraph Graphon theory Markov logic network Large deviation principle Wang, Yuyi aut Ramon, Jan aut Enthalten in Machine learning Springer US, 1986 112(2022), 1 vom: 13. Dez., Seite 177-216 (DE-627)12920403X (DE-600)54638-0 (DE-576)014457377 0885-6125 nnns volume:112 year:2022 number:1 day:13 month:12 pages:177-216 https://doi.org/10.1007/s10994-022-06281-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT AR 112 2022 1 13 12 177-216 |
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10.1007/s10994-022-06281-x doi (DE-627)OLC2080325957 (DE-He213)s10994-022-06281-x-p DE-627 ger DE-627 rakwb eng 150 004 VZ Alvarado, Juan verfasserin (orcid)0000-0002-9794-3675 aut Limits of multi-relational graphs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 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. Large multigraph Graphon theory Markov logic network Large deviation principle Wang, Yuyi aut Ramon, Jan aut Enthalten in Machine learning Springer US, 1986 112(2022), 1 vom: 13. Dez., Seite 177-216 (DE-627)12920403X (DE-600)54638-0 (DE-576)014457377 0885-6125 nnns volume:112 year:2022 number:1 day:13 month:12 pages:177-216 https://doi.org/10.1007/s10994-022-06281-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT AR 112 2022 1 13 12 177-216 |
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10.1007/s10994-022-06281-x doi (DE-627)OLC2080325957 (DE-He213)s10994-022-06281-x-p DE-627 ger DE-627 rakwb eng 150 004 VZ Alvarado, Juan verfasserin (orcid)0000-0002-9794-3675 aut Limits of multi-relational graphs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 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. Large multigraph Graphon theory Markov logic network Large deviation principle Wang, Yuyi aut Ramon, Jan aut Enthalten in Machine learning Springer US, 1986 112(2022), 1 vom: 13. Dez., Seite 177-216 (DE-627)12920403X (DE-600)54638-0 (DE-576)014457377 0885-6125 nnns volume:112 year:2022 number:1 day:13 month:12 pages:177-216 https://doi.org/10.1007/s10994-022-06281-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT AR 112 2022 1 13 12 177-216 |
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10.1007/s10994-022-06281-x doi (DE-627)OLC2080325957 (DE-He213)s10994-022-06281-x-p DE-627 ger DE-627 rakwb eng 150 004 VZ Alvarado, Juan verfasserin (orcid)0000-0002-9794-3675 aut Limits of multi-relational graphs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 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. Large multigraph Graphon theory Markov logic network Large deviation principle Wang, Yuyi aut Ramon, Jan aut Enthalten in Machine learning Springer US, 1986 112(2022), 1 vom: 13. Dez., Seite 177-216 (DE-627)12920403X (DE-600)54638-0 (DE-576)014457377 0885-6125 nnns volume:112 year:2022 number:1 day:13 month:12 pages:177-216 https://doi.org/10.1007/s10994-022-06281-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT AR 112 2022 1 13 12 177-216 |
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10.1007/s10994-022-06281-x doi (DE-627)OLC2080325957 (DE-He213)s10994-022-06281-x-p DE-627 ger DE-627 rakwb eng 150 004 VZ Alvarado, Juan verfasserin (orcid)0000-0002-9794-3675 aut Limits of multi-relational graphs 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 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. Large multigraph Graphon theory Markov logic network Large deviation principle Wang, Yuyi aut Ramon, Jan aut Enthalten in Machine learning Springer US, 1986 112(2022), 1 vom: 13. Dez., Seite 177-216 (DE-627)12920403X (DE-600)54638-0 (DE-576)014457377 0885-6125 nnns volume:112 year:2022 number:1 day:13 month:12 pages:177-216 https://doi.org/10.1007/s10994-022-06281-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT AR 112 2022 1 13 12 177-216 |
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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. © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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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. © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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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. © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Wang, Yuyi Ramon, Jan |
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