{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T08:39:17Z","timestamp":1771490357987,"version":"3.50.1"},"reference-count":96,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"6","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CAREER-1944904"],"award-info":[{"award-number":["CAREER-1944904"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1811868"],"award-info":[{"award-number":["DMS-1811868"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01GM131399"],"award-info":[{"award-number":["R01GM131399"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-1707605"],"award-info":[{"award-number":["DMS-1707605"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-1913149"],"award-info":[{"award-number":["DMS-1913149"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1109\/tit.2022.3152733","type":"journal-article","created":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T20:32:41Z","timestamp":1645216361000},"page":"3991-4019","source":"Crossref","is-referenced-by-count":14,"title":["Optimal High-Order Tensor SVD via Tensor-Train Orthogonal Iteration"],"prefix":"10.1109","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3092-870X","authenticated-orcid":false,"given":"Yuchen","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Wisconsin–Madison, Madison, WI, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8721-5252","authenticated-orcid":false,"given":"Anru R.","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Wisconsin–Madison, Madison, WI, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8274-2304","authenticated-orcid":false,"given":"Lili","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Wisconsin–Madison, Madison, WI, USA"}]},{"given":"Yazhen","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Wisconsin–Madison, Madison, WI, USA"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1214\/17-AOS1659"},{"issue":"2","key":"ref2","first-page":"52","article-title":"Fuzzy dynamic tensor decomposition algorithm for recommender system","volume":"2","author":"Nasiri","year":"2014","journal-title":"UCT J. Res. Sci., Eng. Technol."},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.acn.2007.03.004"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2013.776499"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.21236\/ada604494"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/090748330"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2013.2297439"},{"key":"ref8","first-page":"1051","article-title":"On the connection between learning two-layer neural networks and tensor decomposition","volume-title":"Proc. 22nd Int. Conf. Artif. Intell. Statist.","author":"Mondelli"},{"key":"ref9","article-title":"Learning non-overlapping convolutional neural networks with multiple kernels","author":"Zhong","year":"2017","journal-title":"arXiv:1711.03440"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/ICIP.2010.5651225"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ultramic.2020.113123"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2011.646934"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.tm08439"},{"key":"ref14","article-title":"Tucker tensor layer in fully connected neural networks","author":"Calvi","year":"2019","journal-title":"arXiv:1903.06133"},{"key":"ref15","first-page":"442","article-title":"Tensorizing neural networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Novikov"},{"key":"ref16","first-page":"811","article-title":"Putting MRFs on a tensor train","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Novikov"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/090752286"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02099178"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1134\/S1064562409040115"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1134\/S1064562409040036"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-019-0086-7"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-020-01109-8"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1063\/1.4962420"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.aop.2010.09.012"},{"key":"ref25","first-page":"4799","article-title":"Supervised learning with tensor networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Stoudenmire"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/15M1036919"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.07.024"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1145\/2512329"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/140953289"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975482.172"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2021.113972"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/120885723"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/130942401"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2672439"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/15m1010506"},{"issue":"30","key":"ref36","first-page":"1","article-title":"Tensor train decomposition on TensorFlow (T3F)","volume":"21","author":"Novikov","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1214\/17-AOS1541"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2013.2270464"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1257"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1137\/080738970"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1272"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1214\/15-EJS1076"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2011.04.004"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS618"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2956737"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1137\/s0895479896305696"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898346995"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2018.2841377"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1137\/110836067"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2018.1527227"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1137\/07070111X"},{"key":"ref52","first-page":"3095","article-title":"Orthogonalized ALS: A theoretically principled tensor decomposition algorithm for practical use","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Sharan"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1137\/0614071"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1137\/06065577"},{"key":"ref55","first-page":"2820","article-title":"Tensor decomposition via joint matrix Schur decomposition","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Colombo"},{"key":"ref56","first-page":"79","article-title":"Homotopy analysis for tensor PCA","volume-title":"Proc. Conf. Learn. Theory","author":"Anandkumar"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21861"},{"key":"ref58","first-page":"956","article-title":"Tensor principal component analysis via sum-of-square proofs","volume-title":"Proc. Conf. Learn. Theory","author":"Hopkins"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1214\/21-aos2123"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1214\/19-AIHP960"},{"key":"ref61","first-page":"2897","article-title":"A statistical model for tensor PCA","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Richard"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2017.8006580"},{"key":"ref63","first-page":"27","article-title":"Sparse higher-order principal components analysis","volume-title":"Proc. Artif. Intell. Statist.","author":"Allen"},{"key":"ref64","article-title":"Regularized tensor factorizations and higher-order principal components analysis","author":"Allen","year":"2012","journal-title":"arXiv:1202.2476"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1109\/JSTSP.2018.2873142"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.567"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2019.2891760"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.419"},{"issue":"179","key":"ref69","first-page":"1","article-title":"A sharp blockwise tensor perturbation bound for orthogonal iteration","volume":"22","author":"Luo","year":"2021","journal-title":"J. Mach. Learn. Res."},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2019.000-2"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1137\/16M1074023"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1985.tb01383.x"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1002\/SERIES1345"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2016.2515105"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1042727943"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-013-0738-7"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1109\/CAMSAP45676.2019.9022650"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOS1939"},{"key":"ref79","article-title":"Learning Markov models via low-rank optimization","author":"Zhu","year":"2019","journal-title":"arXiv:1907.00113"},{"key":"ref80","first-page":"996","article-title":"Finite-sample convergence rates for $Q$\n-learning and indirect algorithms","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Kearns"},{"key":"ref81","doi-asserted-by":"publisher","DOI":"10.1145\/1390156.1390191"},{"key":"ref82","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12547"},{"key":"ref83","doi-asserted-by":"publisher","DOI":"10.1016\/j.landurbplan.2012.02.012"},{"key":"ref84","volume-title":"Markov Random Field Modeling in Image Analysis","author":"Li","year":"2009"},{"key":"ref85","doi-asserted-by":"publisher","DOI":"10.1109\/42.906424"},{"key":"ref86","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btm129"},{"key":"ref87","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v29i1.9511"},{"issue":"1","key":"ref88","first-page":"1","article-title":"Graphical models, exponential families, and variational inference","volume":"1","author":"Jordan","year":"2008","journal-title":"Found. Trends Mach. Learn."},{"key":"ref89","doi-asserted-by":"publisher","DOI":"10.1137\/18M1220790"},{"key":"ref90","volume-title":"Markov Decision Processes: Discrete Stochastic Dynamic Programming","author":"Puterman","year":"2014"},{"key":"ref91","first-page":"361","article-title":"Reinforcement learning with soft state aggregation","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Singh"},{"key":"ref92","volume-title":"Introduction to Reinforcement Learning","volume":"135","author":"Sutton","year":"1998"},{"key":"ref93","article-title":"Introduction to the non-asymptotic analysis of random matrices","author":"Vershynin","year":"2010","journal-title":"arXiv:1011.3027"},{"key":"ref94","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOS1178"},{"key":"ref95","doi-asserted-by":"publisher","DOI":"10.1017\/9781108627771"},{"key":"ref96","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2021.08.005"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/18\/9778940\/9717278-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/9778940\/09717278.pdf?arnumber=9717278","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,18]],"date-time":"2024-01-18T00:14:33Z","timestamp":1705536873000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9717278\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6]]},"references-count":96,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.1109\/tit.2022.3152733","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6]]}}}