{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T16:56:59Z","timestamp":1767373019731,"version":"3.34.0"},"reference-count":56,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-21-1-0222"],"award-info":[{"award-number":["FA9550-21-1-0222"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-20-1-2595"],"award-info":[{"award-number":["N00014-20-1-2595"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1745302"],"award-info":[{"award-number":["1745302"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2025,3,31]]},"DOI":"10.1137\/23m159247x","type":"journal-article","created":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T08:34:39Z","timestamp":1738139679000},"page":"189-223","source":"Crossref","is-referenced-by-count":3,"title":["Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices"],"prefix":"10.1137","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-8335-5433","authenticated-orcid":true,"given":"Aimee","family":"Maurais","sequence":"first","affiliation":[{"name":"Center for Computational Science and Engineering, MIT, Cambridge, MA 02139 USA."}]},{"given":"Terrence","family":"Alsup","sequence":"additional","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185 USA."}]},{"given":"Benjamin","family":"Peherstorfer","sequence":"additional","affiliation":[{"name":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185 USA."}]},{"given":"Youssef M.","family":"Marzouk","sequence":"additional","affiliation":[{"name":"Center for Computational Science and Engineering, MIT, Cambridge, MA 02139 USA."}]}],"member":"351","published-online":{"date-parts":[[2025,1,29]]},"reference":[{"key":"ref1","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"Absil P.-A.","year":"2009"},{"key":"ref2","doi-asserted-by":"crossref","DOI":"10.1007\/978-4-431-55978-8","volume-title":"Information Geometry and its Applications","volume":"194","author":"Amari S.-i.","year":"2016"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/mrm.20965","volume":"56","author":"Arsigny V.","year":"2006","journal-title":"Magn. Reson. Med."},{"key":"ref5","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1002\/qj.591","volume":"136","author":"Bergemann K.","year":"2010","journal-title":"Q. J. Roy. Meteorol. Soc."},{"key":"ref6","volume-title":"Positive Definite Matrices","author":"Bhatia R.","year":"2007"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.exmath.2018.01.002","volume":"37","author":"Bhatia R.","year":"2019","journal-title":"Expo. Math."},{"key":"ref8","first-page":"199","volume":"36","author":"Bickel P. J.","year":"2008","journal-title":"Ann. Statist."},{"key":"ref9","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s00211-014-0676-3","volume":"130","author":"Bierig C.","year":"2015","journal-title":"Numer. Math."},{"key":"ref10","first-page":"1455","volume":"15","author":"Boumal N.","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/21M1461551"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s00791-011-0160-x","volume":"14","author":"Cliffe K. A.","year":"2011","journal-title":"Comput. Vis. Sci."},{"key":"ref13","volume-title":"Statistics for Spatial Data","author":"Cressie N.","year":"2015"},{"key":"ref14","volume-title":"Multivariate Extensions of the Multilevel Best Linear Unbiased Estimator for Ensemble-Variational Data Assimilation","author":"Destouches M.","year":"2023"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"1742","DOI":"10.1214\/17-AOS1601","volume":"46","author":"Donoho D.","year":"2018","journal-title":"Ann. Statist."},{"key":"ref17","doi-asserted-by":"crossref","first-page":"17905","DOI":"10.1029\/92JC01972","volume":"97","author":"Evensen G.","year":"1992","journal-title":"J. Geophys. Res.: Oceans"},{"key":"ref18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-03711-5","volume-title":"Data Assimilation: The Ensemble Kalman Filter","author":"Evensen G.","year":"2009"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s11263-012-0591-y","volume":"105","author":"Fletcher P. T.","year":"2013","journal-title":"Int. J. Comput. Vision"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1093\/biostatistics\/kxm045","volume":"9","author":"Friedman J.","year":"2008","journal-title":"Biostatistics"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1002\/qj.49712555417","volume":"125","author":"Gaspari G.","year":"1999","journal-title":"Q. J. Roy. Meteorol. Soc."},{"key":"ref22","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1017\/S096249291500001X","volume":"24","author":"Giles M. B.","year":"2015","journal-title":"Acta Numer."},{"key":"ref23","first-page":"257","volume-title":"in Regularization, Optimization, Kernels, and Support Vector Machines, 12.257","author":"Gillis N.","year":"2014"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"109257","DOI":"10.1016\/j.jcp.2020.109257","volume":"408","author":"Gorodetsky A. A.","year":"2020","journal-title":"J. Comput. Phys."},{"key":"ref26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0022112095000012","volume":"282","author":"Held I.","year":"1985","journal-title":"J. Fluid Mech."},{"key":"ref27","doi-asserted-by":"crossref","unstructured":"N. Higham, Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics, SIAM, Philadelphia, 2008, pp. 269\u2013286, https:\/\/doi.org\/10.1137\/1.9780898717778.ch11.","DOI":"10.1137\/1.9780898717778.ch11"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/15M100955X"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"045001","DOI":"10.1088\/0266-5611\/29\/4\/045001","volume":"29","author":"Iglesias M. A.","year":"2013","journal-title":"Inverse Problems"},{"key":"ref30","doi-asserted-by":"crossref","DOI":"10.1007\/b138659","volume-title":"Statistical and Computational Inverse Problems","volume":"160","author":"Kaipio J.","year":"2005"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","volume":"82","author":"Kalman R. E.","year":"1960","journal-title":"Trans. ASME Ser. D. J. Basic Engrg."},{"key":"ref32","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1561\/2200000019","volume":"5","author":"Kulis B.","year":"2013","journal-title":"Found. Trends\u00ae Mach. Learn."},{"key":"ref33","doi-asserted-by":"crossref","first-page":"1024","DOI":"10.1214\/12-AOS989","volume":"40","author":"Ledoit O.","year":"2012","journal-title":"Ann. Statist."},{"key":"ref34","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1093\/jjfinec\/nbaa007","volume":"20","author":"Ledoit O.","year":"2022","journal-title":"J. Financ. Economet."},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/18M1221084"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/S0898-1221(01)00278-4","volume":"43","author":"Lu T.-T.","year":"2002","journal-title":"Comput. Math. Appl."},{"key":"ref37","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s41884-018-0014-4","volume":"1","author":"Malag\u00f2 L.","year":"2018","journal-title":"Inf. Geom."},{"key":"ref38","first-page":"77","volume":"7","author":"Markowitz H.","year":"1952","journal-title":"J. Finance"},{"key":"ref40","author":"Minka T. P.","year":"2000","journal-title":"Old and New Matrix Algebra Useful for Statistics"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479801383877"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1137\/18M1216389"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1002\/nme.4761","volume":"100","author":"Ng L.","year":"2014","journal-title":"Internat. J. Numer. Methods Engrg."},{"key":"ref44","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1007\/s00211-018-0945-7","volume":"139","author":"Peherstorfer B.","year":"2018","journal-title":"Numer. Math."},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1137\/15M1046472"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1137\/16M1082469"},{"key":"ref47","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10851-006-6228-4","volume":"25","author":"Pennec X.","year":"2006","journal-title":"J. Math. Imaging Vision"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s11263-005-3222-z","volume":"66","author":"Pennec X.","year":"2006","journal-title":"Int. J. Comput. Vision"},{"key":"ref49","first-page":"510","volume":"7","author":"Petersen K. B.","year":"2008","journal-title":"Technical University of Denmark"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1137\/17M1151006"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1038\/nbt0308-303","volume":"26","author":"Ringn\u00e9r M.","year":"2008","journal-title":"Nat. Biotechnol."},{"key":"ref52","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1287\/opre.33.3.661","volume":"33","author":"Rubinstein R. Y.","year":"1985","journal-title":"Oper. Res."},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1137\/19M1263534"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1137\/20M1321607"},{"key":"ref55","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1111\/insr.12113","volume":"84","author":"Schwartzman A.","year":"2016","journal-title":"Int. Stat. Rev."},{"key":"ref56","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1109\/TSP.2005.845428","volume":"53","author":"Smith S. T.","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1137\/140978168"},{"key":"ref58","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71050-9","volume-title":"Optimal Transport: Old and New","volume":"338","author":"Villani C.","year":"2009"},{"key":"ref59","first-page":"207","volume":"10","author":"Weinberger K. Q.","year":"2009","journal-title":"J. Mach. Learn. Res."},{"key":"ref60","volume":"15","author":"Xing E.","year":"2002","journal-title":"Adv. Neural Inf. Process. Syst."}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T08:34:55Z","timestamp":1738139695000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M159247X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,29]]},"references-count":56,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3,31]]}},"alternative-id":["10.1137\/23M159247X"],"URL":"https:\/\/doi.org\/10.1137\/23m159247x","relation":{},"ISSN":["2577-0187"],"issn-type":[{"value":"2577-0187","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,29]]}}}