{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T09:27:05Z","timestamp":1789723625548,"version":"4.0.1"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/501100003443","name":"Ministry of Education and Science of the Russian Federation","doi-asserted-by":"publisher","award":["14.756.31.0001"],"award-info":[{"award-number":["14.756.31.0001"]}],"id":[{"id":"10.13039\/501100003443","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that the tensor is of high order, and tensor values are generated by an unknown smooth function. The assumption allows us to develop an efficient initialization scheme based on Gaussian process regression and the TT-cross approximation technique. The proposed approach can be used in conjunction with any optimization algorithm that is usually utilized in tensor completion problems. We empirically justify that in this case the reconstruction error improves compared to the tensor completion with random initialization. As an additional benefit, our technique automatically selects rank thanks to using the TT-cross approximation technique.<\/jats:p>","DOI":"10.1137\/19m1306518","type":"journal-article","created":{"date-parts":[[2020,12,14]],"date-time":"2020-12-14T11:46:53Z","timestamp":1607946413000},"page":"A3812-A3824","source":"Crossref","is-referenced-by-count":4,"title":["Tensor Completion via Gaussian Process--Based Initialization"],"prefix":"10.1137","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9645-1823","authenticated-orcid":true,"given":"Yermek","family":"Kapushev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ivan","family":"Oseledets","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Evgeny","family":"Burnaev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,12,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.chemolab.2010.08.004"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/140960980"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2016.09.001"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-17091-6_6"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1134\/S0965542516040163"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1134\/S1064226916060061"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2013.164"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/2\/025010"},{"key":"atypb9","volume-title":"Preprint 149","author":"Grasedyck L.","year":"2013"},{"key":"atypb10","volume-title":"Alternating Least Squares Tensor Completion in the TT-Format, preprint, https:\/\/arxiv.org\/abs\/1509.00311","author":"Grasedyck L.","year":"2015"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2020.2995061"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-013-0455-z"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2012.39"},{"key":"atypb14","first-page":"9147","author":"Munkhoeva M.","year":"2018","journal-title":"Advances in Neural Information Processing Systems"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.07.024"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/090752286"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-28650-9_4"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/070697835"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/15M1010506"},{"key":"atypb20","unstructured":"C. Tobler,\n                      Low-Rank Tensor Methods for Linear Systems and Eigenvalue Problems\n                      , Ph.D. thesis, ETH Zurich, 2012."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s006070070031"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2016.2586759"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-70087-8_24"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1109\/TCPMT.2016.2628703"},{"key":"atypb25","volume-title":"High-Dimension Tensor Completion via Gradient-Based Optimization under Tensor-Train Format, preprint, https:\/\/arxiv.org\/abs\/1804.01983","author":"Yuan L.","year":"2018"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2015.2392756"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1306518","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:36:45Z","timestamp":1787326605000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1306518"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":26,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1306518"],"URL":"https:\/\/doi.org\/10.1137\/19m1306518","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}