{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T19:36:19Z","timestamp":1772825779315,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,3,16]],"date-time":"2012-03-16T00:00:00Z","timestamp":1331856000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"published-print":{"date-parts":[[2012,6]]},"DOI":"10.1007\/s11063-012-9217-1","type":"journal-article","created":{"date-parts":[[2012,3,15]],"date-time":"2012-03-15T06:08:51Z","timestamp":1331791731000},"page":"265-281","source":"Crossref","is-referenced-by-count":1,"title":["Learning Rates for Regularized Classifiers Using Trigonometric Polynomial Kernels"],"prefix":"10.1007","volume":"35","author":[{"given":"Feilong","family":"Cao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joonwhoan","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,3,16]]},"reference":[{"key":"9217_CR1","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","volume":"68","author":"N Arouszajiu","year":"1950","unstructured":"Arouszajiu N (1950) Theory of reproducing kernels. Trans Math Soc 68: 337\u2013404","journal-title":"Trans Math Soc"},{"key":"9217_CR2","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1109\/18.661502","volume":"44","author":"PL Bartlett","year":"1998","unstructured":"Bartlett PL (1998) The sample complexity of pattern classificayion with neural networks: the size of the weights is more import than the size of the network. IEEE Trans Inf Theory 44: 525\u2013536","journal-title":"IEEE Trans Inf Theory"},{"key":"9217_CR3","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1017\/S0266466608080225","volume":"24","author":"PL Bartlett","year":"2008","unstructured":"Bartlett PL (2008) Fast rates for estimation error and oracle inequalities for model selection. Econom Theory 24: 545\u2013552","journal-title":"Econom Theory"},{"key":"9217_CR4","first-page":"371","volume":"55","author":"O Bousquet","year":"2003","unstructured":"Bousquet O (2003) New approaches to statistical learning theory. Ann Inst Stat Math 55: 371\u2013389","journal-title":"Ann Inst Stat Math"},{"key":"9217_CR5","first-page":"499","volume":"2","author":"O Bousquet","year":"2002","unstructured":"Bousquet O, Elisseeff A (2002) Stability and generalization. J Mach Learn Res 2: 499\u2013526","journal-title":"J Mach Learn Res"},{"key":"9217_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-7448-9","volume-title":"Fourier analysis and approximation, vol I","author":"PL Butzer","year":"1971","unstructured":"Butzer PL, Nessel RJ (1971) Fourier analysis and approximation, vol I. Birkh\u00e4user\/Academic Press, Basel"},{"key":"9217_CR7","first-page":"1143","volume":"5","author":"DR Chen","year":"2004","unstructured":"Chen DR, Wu Q, Ying YM, Zhou DX (2004) Support vector machine soft margin classifiers: error analysis. J Mach Learn Res 5: 1143\u20131175","journal-title":"J Mach Learn Res"},{"key":"9217_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-01-00923-5","volume":"39","author":"F Cucker","year":"2001","unstructured":"Cucker F, Smale S (2001) On the mathematical foundations of learning theory. Bull Am Math Soc 39: 1\u201349","journal-title":"Bull Am Math Soc"},{"key":"9217_CR9","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s102080010030","volume":"1","author":"F Cucker","year":"2002","unstructured":"Cucker F, Smale S (2002) Best choices for regularization parameters in learning theory: on the biasvariance problem. Found Comput Math 1: 413\u2013428","journal-title":"Found Comput Math"},{"key":"9217_CR10","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511618796","volume-title":"Learning theory: an approximation theory viewpoint","author":"F Cucker","year":"2007","unstructured":"Cucker F, Zhou DX (2007) Learning theory: an approximation theory viewpoint. Cambridge University Press, Cambridge"},{"key":"9217_CR11","volume-title":"A probabilistic theory of pattern recognition","author":"L Devroye","year":"1997","unstructured":"Devroye L, Gyorfi L, Lugosi G (1997) A probabilistic theory of pattern recognition. Springer, New York"},{"key":"9217_CR12","unstructured":"Evgeniou T, Pontil M (1999) On the V-gamma dimension for regression in reproducing Kernel Hilbert spaces. In Proceedings of algorithmic learning theory. Lecture notes in computer science, vol 1720. Springer, London, pp 106\u2013117"},{"key":"9217_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1018946025316","volume":"13","author":"T Evgeniou","year":"2000","unstructured":"Evgeniou T, Pontil M, Poggio T (2000) Regularization networks and support vector machines. Adv Comput Math 13: 1\u201350","journal-title":"Adv Comput Math"},{"key":"9217_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21606-5","volume-title":"The elements of statistical learning: data mining, inference, and prediction","author":"T Hastie","year":"2001","unstructured":"Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning: data mining, inference, and prediction. Springer, New York"},{"issue":"1","key":"9217_CR15","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.csda.2007.02.013","volume":"52","author":"CM Huang","year":"2007","unstructured":"Huang CM, Lee YJ, Lin DKJ, Huang SY (2007) Model selection for support vector machines via uniform design. Comput Stat Data Anal 52(1): 335\u2013346","journal-title":"Comput Stat Data Anal"},{"key":"9217_CR16","unstructured":"Kutin S, Niyogi P (2002) Almost-everywhere algorithmic stability and generalization error. Technical Report TR-2002-03, Department of Computer Science, The University of Chicago"},{"key":"9217_CR17","first-page":"1902","volume":"47","author":"V Koltchinskii","year":"2000","unstructured":"Koltchinskii V, Panchenko D (2000) Rademacher processes and bounding the risk of function learning. High Dimens Probab 47: 1902\u20131914","journal-title":"High Dimens Probab"},{"key":"9217_CR18","volume-title":"Neural network learning: theoretical foundations","author":"A Martinand","year":"1999","unstructured":"Martinand A, Bartlett PL (1999) Neural network learning: theoretical foundations. Cambridge University Press, Cambridge"},{"key":"9217_CR19","first-page":"817","volume":"7","author":"V R\u00e9gis","year":"2006","unstructured":"R\u00e9gis V, Jean-Philippe V (2006) Consistency and convergence rates of one-class SVMs and related algorithms. J Mach Learn Res 7: 817\u2013854","journal-title":"J Mach Learn Res"},{"issue":"4","key":"9217_CR20","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1016\/j.csda.2008.10.037","volume":"53","author":"J Shim","year":"2009","unstructured":"Shim J, Hwang C (2009) Support vector censored quantize regression under random censoring. Comput Stat Data Anal 53(4): 912\u2013919","journal-title":"Comput Stat Data Anal"},{"key":"9217_CR21","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1090\/S0273-0979-04-01025-0","volume":"41","author":"S Smale","year":"2004","unstructured":"Smale S, Zhou DX (2004) Shannon sampling and function reconstruction from point values. Bull Am Math Soc 41: 279\u2013305","journal-title":"Bull Am Math Soc"},{"key":"9217_CR22","first-page":"67","volume":"2","author":"I Steinwart","year":"2001","unstructured":"Steinwart I (2001) On the influence of the kernel on the consistency of support vector machines. J Mach Learn Res 2: 67\u201373","journal-title":"J Mach Learn Res"},{"key":"9217_CR23","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.jco.2008.05.008","volume":"24","author":"HZ Tong","year":"2008","unstructured":"Tong HZ, Chen DR, Li ZP (2008) Learning rates for regularized classifiers using multivariate polynomial kernels. J Complex 24: 619\u2013631","journal-title":"J Complex"},{"key":"9217_CR24","volume-title":"Statistical learning theory","author":"V Vapnik","year":"1998","unstructured":"Vapnik V (1998) Statistical learning theory. Wiley, New York"},{"key":"9217_CR25","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1162\/0899766053491896","volume":"17","author":"Q Wu","year":"2005","unstructured":"Wu Q, Zhou DX (2005) SVM soft margin classifiers: linear programming versus quadratic programming. Neural Comput 17: 1160\u20131187","journal-title":"Neural Comput"},{"key":"9217_CR26","first-page":"108","volume":"8","author":"Q Wu","year":"2006","unstructured":"Wu Q, Zhou DX (2006) Analysis of support vector machine classification. J Comput Anal Appl 8: 108\u2013134","journal-title":"J Comput Anal Appl"},{"key":"9217_CR27","first-page":"291","volume":"3","author":"GB Ye","year":"2008","unstructured":"Ye GB, Zhou DX (2008) Learning and approximation by Gaussian on Riemannian manifolds. Adv Comput Math 3: 291\u2013310","journal-title":"Adv Comput Math"},{"key":"9217_CR28","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.jco.2006.06.007","volume":"23","author":"Q Wu","year":"2007","unstructured":"Wu Q, Ying YM, Zhou DX (2007) Multi-kernel regularized classifiers. J Complex 23: 108\u2013134","journal-title":"J Complex"},{"key":"9217_CR29","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1214\/aos\/1079120130","volume":"32","author":"T Zhang","year":"2004","unstructured":"Zhang T (2004) Statistical behavior and consistency of classification methods based on convex risk minimization. Ann Stat 32: 56\u201385","journal-title":"Ann Stat"},{"key":"9217_CR30","first-page":"1734","volume":"49","author":"DX Zhou","year":"2003","unstructured":"Zhou DX (2003) Capacity of reproducing kernel spaces in learning theory. IEEE Trans Inf Theory 49: 1734\u20131752","journal-title":"IEEE Trans Inf Theory"},{"key":"9217_CR31","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s10444-004-7206-2","volume":"25","author":"DX Zhou","year":"2006","unstructured":"Zhou DX, Jetter K (2006) Approximation with polynomial kernel and SVM classifiers. Adv Comput Math 25: 323\u2013344","journal-title":"Adv Comput Math"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-012-9217-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11063-012-9217-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-012-9217-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,25]],"date-time":"2019-06-25T05:02:02Z","timestamp":1561438922000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11063-012-9217-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,16]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,6]]}},"alternative-id":["9217"],"URL":"https:\/\/doi.org\/10.1007\/s11063-012-9217-1","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"value":"1370-4621","type":"print"},{"value":"1573-773X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,16]]}}}