{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T17:48:46Z","timestamp":1790617726194,"version":"4.1.0"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighbourhood smoothing method requires little tuning, has a competitive mean squared error rate and outperforms many benchmark methods for link prediction in simulated and real networks.<\/jats:p>","DOI":"10.1093\/biomet\/asx042","type":"journal-article","created":{"date-parts":[[2017,8,1]],"date-time":"2017-08-01T07:18:14Z","timestamp":1501571894000},"page":"771-783","source":"Crossref","is-referenced-by-count":62,"title":["Estimating network edge probabilities by neighbourhood smoothing"],"prefix":"10.1093","volume":"104","author":[{"given":"Yuan","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Statistics, Ohio State University, 404 Cockins Hall, 1958 Neil Avenue, Columbus, Ohio 43210, U.S.A, yzhanghf@stat.osu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elizaveta","family":"Levina","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Michigan, 311 West Hall, 1085 South University Avenue, Ann Arbor, Michigan 48109, U.S.A. elevina@umich.edu jizhu@umich.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ji","family":"Zhu","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Michigan, 311 West Hall, 1085 South University Avenue, Ann Arbor, Michigan 48109, U.S.A. elevina@umich.edu jizhu@umich.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,9,15]]},"reference":[{"key":"2019071815503013100_B1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1145\/1134271.1134277","article-title":"The political blogosphere and the 2004 U.S. election: Divided they blog.","volume-title":"Proc. 3rd Int. Workshop on Link Discovery","author":"Adamic","year":"2005"},{"key":"2019071815503013100_B2","first-page":"1981","article-title":"Mixed membership stochastic blockmodels.","volume":"9","author":"Airoldi","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"2019071815503013100_B3","first-page":"692","article-title":"Stochastic blockmodel approximation of a graphon: Theory and consistent estimation.","volume-title":"Advances in Neural Information Processing Systems 26","author":"Airoldi","year":"2013"},{"key":"2019071815503013100_B4","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/0047-259X(81)90099-3","article-title":"Representations for partially exchangeable arrays of random variables.","volume":"11","author":"Aldous","year":"1981","journal-title":"J. Mult. Anal."},{"key":"2019071815503013100_B5","doi-asserted-by":"crossref","first-page":"2097","DOI":"10.1214\/13-AOS1138","article-title":"Pseudo-likelihood methods for community detection in large sparse networks.","volume":"41","author":"Amini","year":"2013","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B6","article-title":"On semidefinite relaxations for the block model.","author":"Amini","year":"2016"},{"key":"2019071815503013100_B7","doi-asserted-by":"crossref","first-page":"21068","DOI":"10.1073\/pnas.0907096106","article-title":"A nonparametric view of network models and Newman\u2013Girvan and other modularities.","volume":"106","author":"Bickel","year":"2009","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2019071815503013100_B8","article-title":"An iterative step-function estimator for graphons.","author":"Cai","year":"2015"},{"key":"2019071815503013100_B9","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1214\/14-AOS1290","article-title":"Robust and computationally feasible community detection in the presence of arbitrary outlier nodes.","volume":"43","author":"Cai","year":"2015","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B10","doi-asserted-by":"crossref","first-page":"2342","DOI":"10.1109\/TIT.2011.2111771","article-title":"Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements.","volume":"57","author":"Cand\u00e8s","year":"2011","journal-title":"IEEE Trans. Info. Theory"},{"key":"2019071815503013100_B11","first-page":"208","article-title":"A consistent histogram estimator for exchangeable graph models.","volume":"32","author":"Chan","year":"2014","journal-title":"J. Mach. Learn. Res. Workshop Conf. Proc."},{"key":"2019071815503013100_B12","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1214\/14-AOS1272","article-title":"Matrix estimation by universal singular value thresholding.","volume":"43","author":"Chatterjee","year":"2015","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B13","first-page":"1","article-title":"Spectral clustering of graphs with general degrees in the extended planted partition model.","volume":"2012","author":"Chaudhuri","year":"2012","journal-title":"J. Mach. Learn. Res."},{"key":"2019071815503013100_B14","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1214\/16-AOS1497","article-title":"Co-clustering of nonsmooth graphons.","volume":"45","author":"Choi","year":"2017","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B15","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1214\/13-AOS1173","article-title":"Co-clustering separately exchangeable network data.","volume":"42","author":"Choi","year":"2014","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B16","article-title":"Graph limits and exchangeable random graphs.","author":"Diaconis","year":"2007"},{"key":"2019071815503013100_B17","first-page":"1","article-title":"Optimal estimation and completion of matrices with biclustering structures.","volume":"17","author":"Gao","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"2019071815503013100_B18","doi-asserted-by":"crossref","first-page":"2624","DOI":"10.1214\/15-AOS1354","article-title":"Rate-optimal graphon estimation.","volume":"43","author":"Gao","year":"2015","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B19","article-title":"A general framework for Bayes structured linear models.","author":"Gao","year":"2015"},{"key":"2019071815503013100_B20","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s00440-015-0659-z","article-title":"Community detection in sparse networks via Grothendieck\u2019s inequality.","volume":"165","author":"Gu\u00e9don","year":"2016","journal-title":"Prob. Theory Rel. Fields"},{"key":"2019071815503013100_B21","first-page":"657","article-title":"Modeling homophily and stochastic equivalence in symmetric relational data.","volume":"20","author":"Hoff","year":"2008","journal-title":"Adv. Neural Info. Proc. Syst."},{"key":"2019071815503013100_B22","first-page":"016107","article-title":"Stochastic blockmodels and community structure in networks.","volume":"E 83","author":"Karrer","year":"2011","journal-title":"Phys. Rev."},{"key":"2019071815503013100_B23","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1214\/16-AOS1454","article-title":"Oracle inequalities for network models and sparse graphon estimation.","volume":"45","author":"Klopp","year":"2017","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B24","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1145\/1835804.1835837","article-title":"New perspectives and methods in link prediction.","volume-title":"Proc. 16th ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining","author":"Lichtenwalter","year":"2010"},{"key":"2019071815503013100_B25","doi-asserted-by":"crossref","first-page":"14722","DOI":"10.1073\/pnas.1400374111","article-title":"Network histograms and universality of blockmodel approximation.","volume":"111","author":"Olhede","year":"2014","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2019071815503013100_B26","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1214\/11-AOS887","article-title":"Spectral clustering and the high-dimensional stochastic blockmodel.","volume":"39","author":"Rohe","year":"2011","journal-title":"Ann. Statist."},{"key":"2019071815503013100_B27","first-page":"406","article-title":"Spectral clustering of graphs with the Bethe Hessian.","volume-title":"Advances in Neural Information Processing Systems 27","author":"Saade","year":"2014"},{"key":"2019071815503013100_B28","article-title":"Nonparametric graphon estimation.","author":"Wolfe","year":"2013"},{"key":"2019071815503013100_B29","first-page":"1060","article-title":"Nonparametric estimation and testing of exchangeable graph models.","volume":"33","author":"Yang","year":"2014","journal-title":"J. Mach. Learn. Res. Workshop Conf. Proc."},{"key":"2019071815503013100_B30","article-title":"Detecting overlapping communities in networks using spectral methods.","author":"Zhang","year":"2015"},{"key":"2019071815503013100_B31","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2017.1286243","article-title":"Link prediction for partially observed networks.","author":"Zhao","year":"2017","journal-title":"J. Comp. Graph. Statist.,"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/104\/4\/771\/21813608\/asx042.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,31]],"date-time":"2022-07-31T13:56:01Z","timestamp":1659275761000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/104\/4\/771\/4158787"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,15]]},"references-count":31,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,9,15]]},"published-print":{"date-parts":[[2017,12,1]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asx042","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2017,12]]},"published":{"date-parts":[[2017,9,15]]}}}