{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T23:17:36Z","timestamp":1776122256595,"version":"3.50.1"},"reference-count":65,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"3","license":[{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"},{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1750362"],"award-info":[{"award-number":["1750362"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE J. Sel. Areas Inf. Theory"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1109\/jsait.2020.3040598","type":"journal-article","created":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T21:10:00Z","timestamp":1606770600000},"page":"777-798","source":"Crossref","is-referenced-by-count":24,"title":["Information-Theoretic Limits for the Matrix Tensor Product"],"prefix":"10.1109","volume":"1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4230-0688","authenticated-orcid":false,"given":"Galen","family":"Reeves","sequence":"first","affiliation":[]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2054430"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-002-0773-5"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2015.7447070"},{"key":"ref32","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-22253-5","author":"talagrand","year":"2011","journal-title":"Mean field models for spin glasses Volume II Advanced replica symmetry and low temperature"},{"key":"ref31","author":"talagrand","year":"2011","journal-title":"Mean Field Models for Spin Glasses Volume I Basic Examples"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198570837.001.0001"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-002-0699-y"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ab2735"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-018-0879-0"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/aa7284"},{"key":"ref60","author":"magnus","year":"2007","journal-title":"Matrix Differential Calculus with Applications in Statistics and Econometrics"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9305-4"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719222"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(70)90156-7"},{"key":"ref28","first-page":"8364","article-title":"The spiked matrix model with generative priors","author":"aubin","year":"2019","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00296"},{"key":"ref27","author":"barbier","year":"2019","journal-title":"0–1 phase transitions in sparse spiked matrix estimation"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199535255.001.0001"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/ITW44776.2019.8989408"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0121"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1009210544"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2018.8437810"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1214\/19-AAP1556"},{"key":"ref21","author":"mourrat","year":"2018","journal-title":"Hamilton-jacobi equations for mean-field disordered systems"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2019.8849594"},{"key":"ref23","author":"reeves","year":"2019","journal-title":"Understanding phase transitions via mutual information and MMSE"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2019.8919733"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2019.8849594"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2018.8437326"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.844072"},{"key":"ref59","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-48311-5","author":"bauschke","year":"2017","journal-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2090193"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iaaa008"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2562630"},{"key":"ref54","doi-asserted-by":"crossref","first-page":"2371","DOI":"10.1109\/TIT.2011.2111010","article-title":"Estimation in Gaussian noise: Properties of the minimum mean-square error","volume":"57","author":"guo","year":"2011","journal-title":"IEEE Trans Inf Theory"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2009.2023749"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.860424"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2016.7541382"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2016.7852290"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2206794"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2891664"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1802705116"},{"key":"ref14","first-page":"125","article-title":"Asymptotic mutual information for the balanced binary stochastic block model","volume":"6","author":"deshpande","year":"2017","journal-title":"Inf Inference"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/ITW.2016.7606798"},{"key":"ref16","first-page":"424","article-title":"Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula","volume":"29","author":"barbier","year":"2016","journal-title":"Proc Adv Neural Inf Process Syst (NIPS)"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-018-0845-x"},{"key":"ref18","author":"miolane","year":"2017","journal-title":"Fundamental limits of symmetric low-rank matrix estimation"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2017.8262855"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2016.7852287"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1198\/106186006X113430"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.066106"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2018.2810020"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2070131"},{"key":"ref7","first-page":"1","article-title":"Community detection and stochastic block models: Recent developments","volume":"18","author":"abbe","year":"2018","journal-title":"J Mach Learn Res"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1109\/ISWCS.2009.5285230"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2015.7282733"},{"key":"ref46","first-page":"334","article-title":"Sparse PCA via covariance thresholding","author":"deshpande","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2014.6875223"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT44484.2020.9173970"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1214\/17-AOS1625"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS664"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1214\/009117905000000233"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iax014"},{"key":"ref43","first-page":"1246","article-title":"Iterative reconstruction of rank-one matrices in noise","author":"fletcher","year":"2012","journal-title":"Proc IEEE Int Symp Inf Theory"}],"container-title":["IEEE Journal on Selected Areas in Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/8700143\/9319601\/9272982-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/8700143\/9319601\/09272982.pdf?arnumber=9272982","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,14]],"date-time":"2023-10-14T08:28:21Z","timestamp":1697272101000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9272982\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11]]},"references-count":65,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1109\/jsait.2020.3040598","relation":{},"ISSN":["2641-8770"],"issn-type":[{"value":"2641-8770","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11]]}}}