{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:41:31Z","timestamp":1742913691671,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":31,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662448472"},{"type":"electronic","value":"9783662448489"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-662-44848-9_23","type":"book-chapter","created":{"date-parts":[[2014,9,1]],"date-time":"2014-09-01T01:42:21Z","timestamp":1409535741000},"page":"354-369","source":"Crossref","is-referenced-by-count":4,"title":["Approximate Consistency: Towards Foundations of Approximate Kernel Selection"],"prefix":"10.1007","author":[{"given":"Lizhong","family":"Ding","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shizhong","family":"Liao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"23_CR1","volume-title":"Introduction to Machine Learning","author":"E. Alpaydin","year":"2004","unstructured":"Alpaydin, E.: Introduction to Machine Learning. MIT Press, Cambridge (2004)"},{"key":"23_CR2","unstructured":"Bach, F.: Sharp analysis of low-rank kernel matrix approximations. In: Proceedings of the 26th Annual Conference on Learning Theory (COLT), pp. 185\u2013209 (2013)"},{"issue":"1\u20133","key":"23_CR3","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1023\/A:1013999503812","volume":"48","author":"P.L. Bartlett","year":"2002","unstructured":"Bartlett, P.L., Boucheron, S., Lugosi, G.: Model selection and error estimation. Machine Learning\u00a048(1\u20133), 85\u2013113 (2002)","journal-title":"Machine Learning"},{"key":"23_CR4","first-page":"463","volume":"3","author":"P. Bartlett","year":"2002","unstructured":"Bartlett, P., Mendelson, S.: Rademacher and Gaussian complexities: Risk bounds and structural results. Journal of Machine Learning Research\u00a03, 463\u2013482 (2002)","journal-title":"Journal of Machine Learning Research"},{"key":"23_CR5","first-page":"2079","volume":"11","author":"G. Cawley","year":"2010","unstructured":"Cawley, G., Talbot, N.: On over-fitting in model selection and subsequent selection bias in performance evaluation. Journal of Machine Learning Research\u00a011, 2079\u20132107 (2010)","journal-title":"Journal of Machine Learning Research"},{"issue":"1-3","key":"23_CR6","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1023\/A:1012450327387","volume":"46","author":"O. Chapelle","year":"2002","unstructured":"Chapelle, O., Vapnik, V., Bousquet, O., Mukherjee, S.: Choosing multiple parameters for support vector machines. Machine Learning\u00a046(1-3), 131\u2013159 (2002)","journal-title":"Machine Learning"},{"key":"23_CR7","unstructured":"Cortes, C., Mohri, M., Talwalkar, A.: On the impact of kernel approximation on learning accuracy. In: Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS), pp. 113\u2013120 (2010)"},{"issue":"1","key":"23_CR8","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s10208-004-0134-1","volume":"5","author":"E. Vito De","year":"2005","unstructured":"De Vito, E., Caponnetto, A., Rosasco, L.: Model selection for regularized least-squares algorithm in learning theory. Foundations of Computational Mathematics\u00a05(1), 59\u201385 (2005)","journal-title":"Foundations of Computational Mathematics"},{"key":"23_CR9","first-page":"165","volume":"20","author":"L.Z. Ding","year":"2011","unstructured":"Ding, L.Z., Liao, S.Z.: Approximate model selection for large scale LSSVM. Journal of Machine Learning Research - Proceedings Track\u00a020, 165\u2013180 (2011)","journal-title":"Journal of Machine Learning Research - Proceedings Track"},{"key":"23_CR10","series-title":"LNAI","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1007\/978-3-642-30217-6_24","volume-title":"Advances in Knowledge Discovery and Data Mining","author":"L. Ding","year":"2012","unstructured":"Ding, L., Liao, S.: Nystr\u00f6m approximate model selection for LSSVM. In: Tan, P.-N., Chawla, S., Ho, C.K., Bailey, J. (eds.) PAKDD 2012, Part I. LNCS (LNAI), vol.\u00a07301, pp. 282\u2013293. Springer, Heidelberg (2012)"},{"key":"23_CR11","first-page":"2153","volume":"6","author":"P. Drineas","year":"2005","unstructured":"Drineas, P., Mahoney, M.W.: On the Nystr\u00f6m method for approximating a Gram matrix for improved kernel-based learning. Journal of Machine Learning Research\u00a06, 2153\u20132175 (2005)","journal-title":"Journal of Machine Learning Research"},{"key":"23_CR12","first-page":"243","volume":"2","author":"S. Fine","year":"2002","unstructured":"Fine, S., Scheinberg, K.: Efficient SVM training using low-rank kernel representations. Journal of Machine Learning Research\u00a02, 243\u2013264 (2002)","journal-title":"Journal of Machine Learning Research"},{"key":"23_CR13","unstructured":"Gittens, A., Mahoney, M.W.: Revisiting the Nystr\u00f6m method for improved large-scale machine learning. In: Proceedings of the 30th International Conference on Machine Learning (ICML), pp. 567\u2013575 (2013)"},{"issue":"2","key":"23_CR14","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1080\/00401706.1979.10489751","volume":"21","author":"G.H. Golub","year":"1979","unstructured":"Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics\u00a021(2), 215\u2013223 (1979)","journal-title":"Technometrics"},{"key":"23_CR15","first-page":"1391","volume":"5","author":"T. Hastie","year":"2004","unstructured":"Hastie, T., Rosset, S., Tibshirani, R., Zhu, J.: The entire regularization path for the support vector machine. Journal of Machine Learning Research\u00a05, 1391\u20131415 (2004)","journal-title":"Journal of Machine Learning Research"},{"issue":"10","key":"23_CR16","doi-asserted-by":"publisher","first-page":"6939","DOI":"10.1109\/TIT.2013.2271378","volume":"5","author":"R. Jin","year":"2013","unstructured":"Jin, R., Yang, T.B., Mahdavi, M., Li, Y.F., Zhou, Z.H.: Improved bounds for the Nystr\u00f6m method with application to kernel classification. IEEE Transactions on Information Theory\u00a05(10), 6939\u20136949 (2013)","journal-title":"IEEE Transactions on Information Theory"},{"key":"23_CR17","first-page":"981","volume":"13","author":"S. Kumar","year":"2012","unstructured":"Kumar, S., Mohri, M., Talwalkar, A.: Sampling methods for the Nystr\u00f6m method. Journal of Machine Learning Research\u00a013, 981\u20131006 (2012)","journal-title":"Journal of Machine Learning Research"},{"key":"23_CR18","unstructured":"Liu, Y., Jiang, S., Liao, S.: Efficient approximation of cross-validation for kernel methods using Bouligand influence function. In: Proceedings of the 31st International Conference on Machine Learning (ICML), pp. 324\u2013332 (2014)"},{"key":"23_CR19","first-page":"293","volume":"5","author":"U.V. Luxburg","year":"2004","unstructured":"Luxburg, U.V., Bousquet, O., Sch\u00f6lkopf, B.: A compression approach to support vector model selection. Journal of Machine Learning Research\u00a05, 293\u2013323 (2004)","journal-title":"Journal of Machine Learning Research"},{"key":"23_CR20","first-page":"1099","volume":"6","author":"C.A. Micchelli","year":"2005","unstructured":"Micchelli, C.A., Pontil, M.: Learning the kernel function via regularization. Journal of Machine Learning Research\u00a06, 1099\u20131125 (2005)","journal-title":"Journal of Machine Learning Research"},{"key":"23_CR21","volume-title":"Machine Learning","author":"T.M. Mitchell","year":"1997","unstructured":"Mitchell, T.M.: Machine Learning. McGraw Hill, New York (1997)"},{"key":"23_CR22","unstructured":"Smola, A.J., Sch\u00f6lkopf, B.: Sparse greedy matrix approximation for machine learning. In: Proceedings of the 17th International Conference on Machine Learning (ICML), pp. 911\u2013918 (2000)"},{"key":"23_CR23","unstructured":"Song, G.H.: Approximation of kernel matrices in machine learning. Ph.D. thesis, Syracuse University, Syracuse, NY, USA (2010)"},{"issue":"4","key":"23_CR24","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/j.jco.2010.02.003","volume":"26","author":"G.H. Song","year":"2010","unstructured":"Song, G.H., Xu, Y.S.: Approximation of high-dimensional kernel matrices by multilevel circulant matrices. Journal of Complexity\u00a026(4), 375\u2013405 (2010)","journal-title":"Journal of Complexity"},{"key":"23_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0024-3795(94)00025-5","volume":"232","author":"E.E. Tyrtyshnikov","year":"1996","unstructured":"Tyrtyshnikov, E.E.: A unifying approach to some old and new theorems on distribution and clustering. Linear Algebra and its Applications\u00a0232, 1\u201343 (1996)","journal-title":"Linear Algebra and its Applications"},{"key":"23_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2440-0","volume-title":"The Nature of Statistical Learning Theory","author":"V. Vapnik","year":"1995","unstructured":"Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)"},{"key":"23_CR27","volume-title":"Advances in Large Margin Classifiers","author":"G. Wahba","year":"1999","unstructured":"Wahba, G., Lin, Y., Zhang, H.: GACV for support vector machines. In: Advances in Large Margin Classifiers. MIT Press, Cambridge (1999)"},{"key":"23_CR28","first-page":"2729","volume":"14","author":"S.S. Wang","year":"2013","unstructured":"Wang, S.S., Zhang, Z.H.: Improving CUR matrix decomposition and the Nystr\u00f6m approximation via adaptive sampling. Journal of Machine Learning Research\u00a014, 2729\u20132769 (2013)","journal-title":"Journal of Machine Learning Research"},{"key":"23_CR29","unstructured":"Williams, C.K.I., Seeger, M.: Using the Nystr\u00f6m method to speed up kernel machines. In: Advances in Neural Information Processing Systems 13, pp. 682\u2013688 (2001)"},{"key":"23_CR30","unstructured":"Yang, T.B., Li, Y.F., Mahdavi, M., Jin, R., Zhou, Z.H.: Nystr\u00f6m method vs random Fourier features: A theoretical and empirical comparison. In: Advances in Neural Information Processing Systems 24, pp. 1060\u20131068 (2012)"},{"issue":"10","key":"23_CR31","doi-asserted-by":"publisher","first-page":"1576","DOI":"10.1109\/TNN.2010.2064786","volume":"21","author":"K. Zhang","year":"2010","unstructured":"Zhang, K., Kwok, J.T.: Clustered Nystr\u00f6m method for large scale manifold learning and dimension reduction. IEEE Transactions on Neural Networks\u00a021(10), 1576\u20131587 (2010)","journal-title":"IEEE Transactions on Neural Networks"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-44848-9_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,14]],"date-time":"2019-09-14T20:06:01Z","timestamp":1568491561000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-44848-9_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783662448472","9783662448489"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-44848-9_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}