Smoothing graphons for modelling exchangeable relational data

Li, Y; Fan, X; Chen, L; Li, B; Sisson, SA

Smoothing graphons for modelling exchangeable relational data

Li, Y Fan, X Chen, L

Li, B Sisson, SA

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Publisher:: Springer Science and Business Media LLC
Publication Type:: Journal Article
Citation:: Machine Learning, 2021, 111, (1), pp. 319-344
Issue Date:: 2021-08-24

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Field	Value	Language
dc.contributor.author	Li, Y
dc.contributor.author	Fan, X
dc.contributor.author	Chen, L https://orcid.org/0000-0002-6468-5729
dc.contributor.author	Li, B
dc.contributor.author	Sisson, SA
dc.date.accessioned	2022-05-19T00:13:16Z
dc.date.available	2022-05-19T00:13:16Z
dc.date.issued	2021-08-24
dc.identifier.citation	Machine Learning, 2021, 111, (1), pp. 319-344
dc.identifier.issn	0885-6125
dc.identifier.issn	1573-0565
dc.identifier.uri	http://hdl.handle.net/10453/157510
dc.description.abstract	Modelling exchangeable relational data can be described appropriately in graphon theory. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the graphons adopted by existing Bayesian methods are either piecewise-constant functions, which are insufficiently flexible for accurate modelling of the relational data, or are complicated continuous functions, which incur heavy computational costs for inference. In this work, we overcome these two shortcomings by smoothing piecewise-constant graphons, which permits continuous intensity values for describing relations, without impractically increasing computational costs. In particular, we focus on the Bayesian Stochastic Block Model (SBM) and demonstrate how to adapt the piecewise-constant SBM graphon to the smoothed version. We first propose the Integrated Smoothing Graphon (ISG) which introduces one smoothing parameter to the SBM graphon to generate continuous relational intensity values. Then, we further develop the Latent Feature Smoothing Graphon (LFSG), which improves the ISG, by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference. Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision for link prediction without increasing computational complexity.
dc.language	en
dc.publisher	Springer Science and Business Media LLC
dc.relation	http://purl.org/au-research/grants/arc/CE140100049
dc.relation.ispartof	Machine Learning
dc.relation.isbasedon	10.1007/s10994-021-06046-y
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	This is a post-peer-review, pre-copyedit version of a Journal article published in the Machine Learning The final authenticated version is available online at: https://link.springer.com/article/10.1007/s10994-021-06046-y
dc.subject	0801 Artificial Intelligence and Image Processing, 0806 Information Systems, 1702 Cognitive Sciences
dc.subject.classification	Artificial Intelligence & Image Processing
dc.title	Smoothing graphons for modelling exchangeable relational data
dc.type	Journal Article
utslib.citation.volume	111
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0806 Information Systems
utslib.for	1702 Cognitive Sciences
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - AAII - Australian Artificial Intelligence Institute
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
utslib.copyright.status	open_access	*
dc.date.updated	2022-05-19T00:13:14Z
pubs.issue	1
pubs.publication-status	Published
pubs.volume	111
utslib.citation.issue	1

Abstract:

Modelling exchangeable relational data can be described appropriately in graphon theory. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the graphons adopted by existing Bayesian methods are either piecewise-constant functions, which are insufficiently flexible for accurate modelling of the relational data, or are complicated continuous functions, which incur heavy computational costs for inference. In this work, we overcome these two shortcomings by smoothing piecewise-constant graphons, which permits continuous intensity values for describing relations, without impractically increasing computational costs. In particular, we focus on the Bayesian Stochastic Block Model (SBM) and demonstrate how to adapt the piecewise-constant SBM graphon to the smoothed version. We first propose the Integrated Smoothing Graphon (ISG) which introduces one smoothing parameter to the SBM graphon to generate continuous relational intensity values. Then, we further develop the Latent Feature Smoothing Graphon (LFSG), which improves the ISG, by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference. Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision for link prediction without increasing computational complexity.

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http://hdl.handle.net/10453/157510