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Chung J, Varjavand B, Arroyo‐Relión J, Alyakin A, Agterberg J, Tang M, Priebe CE, Vogelstein JT. Valid two‐sample graph testing via optimal transport Procrustes and multiscale graph correlation with applications in connectomics. Stat (Int Stat Inst) 2022. [DOI: 10.1002/sta4.429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Jaewon Chung
- Department of Biomedical Engineering Johns Hopkins University MD 21218 USA
| | - Bijan Varjavand
- Department of Biomedical Engineering Johns Hopkins University MD 21218 USA
| | | | - Anton Alyakin
- Department of Applied Mathematics and Statistics Johns Hopkins University MD 21218 USA
| | - Joshua Agterberg
- Department of Applied Mathematics and Statistics Johns Hopkins University MD 21218 USA
| | - Minh Tang
- Department of Statistics North Carolina State University NC 27695 USA
| | - Carey E. Priebe
- Department of Applied Mathematics and Statistics Johns Hopkins University MD 21218 USA
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Chandna S, Olhede SC, Wolfe PJ. Local linear graphon estimation using covariates. Biometrika 2021. [DOI: 10.1093/biomet/asab057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Summary
We consider local linear estimation of the graphon function, which determines probabilities of pairwise edges between nodes in an unlabelled network. Real-world networks are typically characterized by node heterogeneity, with different nodes exhibiting different degrees of interaction. Existing approaches to graphon estimation are limited to local constant approximations, and are not designed to estimate heterogeneity across the full network. In this paper, we show how continuous node covariates can be employed to estimate heterogeneity in the network via a local linear graphon estimator. We derive the bias and variance of an oracle-based local linear graphon estimator, and thus obtain the mean integrated squared error optimal bandwidth rule. We also provide a plug-in bandwidth selection procedure that makes local linear estimation for unlabelled networks practically feasible. The finite-sample performance of our approach is investigated in a simulation study, and the method is applied to a school friendship network and an email network to illustrate its advantages over existing methods.
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Affiliation(s)
- S Chandna
- Department of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London WC1E 7HX, U.K
| | - S C Olhede
- Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland
| | - P J Wolfe
- Department of Statistics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907, U.S.A
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