{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T10:37:31Z","timestamp":1763116651337},"reference-count":33,"publisher":"MIT Press","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:p>In this letter, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, and (2) approximate the estimator using a few variables by [Formula: see text]-type penalized estimation. We see that the proposed method can be applied to various kernel nonparametric estimation such as kernel ridge regression, kernel-based density, and density-ratio estimation. We prove that the proposed method has the property of variable selection consistency when the power series kernel is used. Here, the power series kernel is a certain class of kernels containing polynomial and exponential kernels. This result is regarded as an extension of the variable selection consistency for the nonnegative garrote (NNG), a special case of the adaptive Lasso, to the kernel-based estimators. Several experiments, including simulation studies and real data applications, show the effectiveness of the proposed method.<\/jats:p>","DOI":"10.1162\/neco_a_01212","type":"journal-article","created":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T18:53:11Z","timestamp":1562007191000},"page":"1718-1750","source":"Crossref","is-referenced-by-count":2,"title":["Variable Selection for Nonparametric Learning with Power Series Kernels"],"prefix":"10.1162","volume":"31","author":[{"given":"Kota","family":"Matsui","sequence":"first","affiliation":[{"name":"RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo 103-0027, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wataru","family":"Kumagai","sequence":"additional","affiliation":[{"name":"RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo 103-0027, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenta","family":"Kanamori","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mitsuaki","family":"Nishikimi","sequence":"additional","affiliation":[{"name":"Department of Emergency and Critical Care, Nagoya University Graduate School of Medicine, Showa-ku, Nagoya 466-8550, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takafumi","family":"Kanamori","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computing Science, Tokyo Institute of Technology, Meguro-ku, Tokyo, 152-8550, and RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo 103-0027, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2012.681213"},{"key":"B2","volume-title":"Reproducing kernel Hilbert spaces in probability and statistics.","author":"Berlinet A.","year":"2003"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1995.10484371"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-006-0196-8"},{"key":"B5","author":"Dheeru D.","year":"2017","journal-title":"UCI machine learning repository."},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12518"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00812"},{"key":"B8","first-page":"569","volume-title":"Advances in neural information processing systems","volume":"15","author":"Grandvalet Y.","year":"2003"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1162\/153244303322753616"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-011-5266-3"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1186\/s13049-017-0392-y"},{"key":"B12","first-page":"2825","volume":"12","author":"Pedregosa F.","year":"2011","journal-title":"Journal of Machine Learning Research"},{"key":"B13","author":"Raschka S.","year":"2016","journal-title":"Mlxtend."},{"key":"B14","first-page":"905","volume":"11","author":"Rosasco L.","year":"2010","journal-title":"Journal of Machine Learning Research"},{"issue":"1","key":"B15","first-page":"1665","volume":"14","author":"Rosasco L.","year":"2013","journal-title":"Journal of Machine Learning Research"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2003.809398"},{"key":"B17","volume-title":"The principles of mathematical analysis","author":"Rudin W.","year":"2006","edition":"3"},{"key":"B18","author":"Salzo S.","year":"2017","journal-title":"Solving -norm regularization with tensor kernels"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(00)00115-4"},{"issue":"57","key":"B20","first-page":"1","volume":"18","author":"Sriperumbudur B.","year":"2017","journal-title":"Journal of Machine Learning Research"},{"key":"B21","volume-title":"Support vector machines.","author":"Steinwart I.","year":"2008"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/781670"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139035613"},{"issue":"1","key":"B24","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"Tibshirani R.","year":"1996","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"B25","volume-title":"Empirical processes in M-estimation","author":"van de Geer S.","year":"2000"},{"key":"B26","volume-title":"Asymptotic statistics","author":"van der Vaart A. 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