{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T01:44:40Z","timestamp":1790646280735,"version":"4.1.0"},"reference-count":62,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"2","license":[{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["Sequoia (724063)"],"award-info":[{"award-number":["Sequoia (724063)"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1109\/tit.2022.3211077","type":"journal-article","created":{"date-parts":[[2022,10,3]],"date-time":"2022-10-03T20:32:07Z","timestamp":1664829127000},"page":"752-775","source":"Crossref","is-referenced-by-count":15,"title":["Information Theory With Kernel Methods"],"prefix":"10.1109","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8644-1058","authenticated-orcid":false,"given":"Francis","family":"Bach","sequence":"first","affiliation":[{"name":"Computer Science Department, Ecole Normale Supérieure, Inria and PSL Research University, Paris, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref39","first-page":"3215","article-title":"Generalization properties of learning with random features","author":"rudi","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref38","author":"kato","year":"1966","journal-title":"Perturbation Theory for Linear Operators"},{"key":"ref33","author":"cover","year":"1999","journal-title":"Elements of Information Theory"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/18.850703"},{"key":"ref31","first-page":"229","article-title":"Information-type measures of difference of probability distributions and indirect observation","volume":"2","author":"csisz\u00e1r","year":"1967","journal-title":"Studia Scientiarum Mathematicarum Hungarica"},{"key":"ref30","author":"yu","year":"2013","journal-title":"The strong convexity of von Neumann's entropy"},{"key":"ref37","article-title":"Less is more: Nyström computational regularization","volume":"28","author":"rudi","year":"2015","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref36","article-title":"Using the Nyström method to speed up kernel machines","volume":"13","author":"williams","year":"2000","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973068.105"},{"key":"ref34","first-page":"1663","article-title":"Relating leverage scores and density using regularized Christoffel functions","author":"pauwels","year":"2018","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1561\/2200000048"},{"key":"ref62","first-page":"714","article-title":"On the equivalence between kernel quadrature rules and random feature expansions","volume":"18","author":"bach","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/BF01212345"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(79)90179-4"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1515\/9781400827787"},{"key":"ref29","first-page":"265","article-title":"Calibrating noise to sensitivity in private data analysis","author":"dwork","year":"2006","journal-title":"Proc Theory Cryptogr Conf"},{"key":"ref2","author":"berlinet","year":"2011","journal-title":"Reproducing Kernel Hilbert Spaces in Probability and Statistics"},{"key":"ref1","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4175.001.0001","author":"sch\u00f6lkopf","year":"2001","journal-title":"Learning with kernels"},{"key":"ref20","first-page":"308","article-title":"Regularization with dot-product kernels","author":"smola","year":"2001","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895290954"},{"key":"ref21","first-page":"629","article-title":"Breaking the curse of dimensionality with convex neural networks","volume":"18","author":"bach","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139525343"},{"key":"ref23","author":"isham","year":"2001","journal-title":"Lectures on Quantum Theory Mathematical and Structural Foundations"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(67)90040-7"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-55925-9_4"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"ref51","first-page":"4620","article-title":"Non-convex optimization with certificates and fast rates through kernel sums of squares","author":"woodworth","year":"2022","journal-title":"Proc 19th Ann Conf Learning Theory (COLT)"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1016\/S0034-4877(07)00019-5"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1063\/1.533053"},{"key":"ref57","article-title":"Infinite-dimensional sums-of-squares for optimal control","author":"berthier","year":"2021","journal-title":"arXiv 2110 07396"},{"key":"ref56","first-page":"4143","article-title":"A dimension-free computational upper-bound for smooth optimal transport estimation","author":"vacher","year":"2021","journal-title":"Proc Conf Learn Theory"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1063\/1.4838835"},{"key":"ref54","doi-asserted-by":"crossref","DOI":"10.1063\/1.4838856","article-title":"On quantum Rényi entropies: A new generalization and some properties","volume":"54","author":"m\u00fcller-lennert","year":"2013","journal-title":"J Math Phys"},{"key":"ref53","article-title":"Semidefinite relaxations for approximate inference on graphs with cycles","volume":"16","author":"jordan","year":"2003","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7712-1"},{"key":"ref10","author":"wainwright","year":"2008","journal-title":"Graphical models exponential families and variational inference"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOS1927"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809682"},{"key":"ref12","first-page":"111","article-title":"Injective Hilbert space embeddings of probability measures","author":"sriperumbudur","year":"2008","journal-title":"Proc 19th Ann Conf Learning Theory (COLT)"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS637"},{"key":"ref14","first-page":"67","article-title":"On the influence of the kernel on the consistency of support vector machines","volume":"2","author":"steinwart","year":"2002","journal-title":"J Mach Learn Res"},{"key":"ref15","author":"reed","year":"1980","journal-title":"Functional Analysis"},{"key":"ref16","author":"brezis","year":"1980","journal-title":"Analyse Fonctionelle"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-86664-8_5"},{"key":"ref18","volume":"115","author":"berger","year":"2012","journal-title":"Differential Geometry Manifolds Curves and Surfaces Manifolds Curves and Surfaces"},{"key":"ref19","author":"h\u00f6rmander","year":"1984","journal-title":"The Analysis of Linear Partial Differential Operators I Distribution Theory and Fourier Analysis"},{"key":"ref4","first-page":"2651","article-title":"Universal kernels","volume":"7","author":"micchelli","year":"2006","journal-title":"J Mach Learn Res"},{"key":"ref3","first-page":"1517","article-title":"Hilbert space embeddings and metrics on probability measures","volume":"11","author":"sriperumbudur","year":"2010","journal-title":"J Mach Learn Res"},{"key":"ref6","first-page":"1177","article-title":"Dependence, correlation and Gaussianity in independent component analysis","volume":"4","author":"cardoso","year":"2003","journal-title":"J Mach Learn Res"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1561\/2200000060"},{"key":"ref8","first-page":"1393","article-title":"Feature selection via dependence maximization","volume":"13","author":"song","year":"2012","journal-title":"J Mach Learn Res"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0552-5"},{"key":"ref7","first-page":"1","article-title":"Kernel independent component analysis","volume":"3","author":"bach","year":"2002","journal-title":"J Mach Learn Res"},{"key":"ref9","article-title":"Demystifying MMD GANs","author":"bi?kowski","year":"2018","journal-title":"Proc Int Conf Learn Represent"},{"key":"ref46","first-page":"489","article-title":"Kernel measures of conditional dependence","volume":"20","author":"fukumizu","year":"2007","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1561\/2200000039"},{"key":"ref48","article-title":"Finding global minima via kernel approximations","author":"rudi","year":"2020","journal-title":"arXiv 2012 11978"},{"key":"ref47","volume":"2","author":"robert","year":"2007","journal-title":"The Bayesian Choice From Decision-Theoretic Foundations to Computational Implementation"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.3390\/e10030261"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1145\/1102351.1102356"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1063\/1.1497701"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1142\/S0129055X03001576"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/10024105\/09908581.pdf?arnumber=9908581","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,5]],"date-time":"2024-10-05T04:49:46Z","timestamp":1728103786000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9908581\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2]]},"references-count":62,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1109\/tit.2022.3211077","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2]]}}}