{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T22:40:02Z","timestamp":1719614402252},"reference-count":27,"publisher":"MIT Press","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2018,2]]},"abstract":"<jats:p>Sufficient dimension reduction (SDR) is aimed at obtaining the low-rank projection matrix in the input space such that information about output data is maximally preserved. Among various approaches to SDR, a promising method is based on the eigendecomposition of the outer product of the gradient of the conditional density of output given input. In this letter, we propose a novel estimator of the gradient of the logarithmic conditional density that directly fits a linear-in-parameter model to the true gradient under the squared loss. Thanks to this simple least-squares formulation, its solution can be computed efficiently in a closed form. Then we develop a new SDR method based on the proposed gradient estimator. We theoretically prove that the proposed gradient estimator, as well as the SDR solution obtained from it, achieves the optimal parametric convergence rate. Finally, we experimentally demonstrate that our SDR method compares favorably with existing approaches in both accuracy and computational efficiency on a variety of artificial and benchmark data sets.<\/jats:p>","DOI":"10.1162\/neco_a_01035","type":"journal-article","created":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T01:20:26Z","timestamp":1511313626000},"page":"477-504","source":"Crossref","is-referenced-by-count":1,"title":["Sufficient Dimension Reduction via Direct Estimation of the Gradients of Logarithmic Conditional Densities"],"prefix":"10.1162","volume":"30","author":[{"given":"Hiroaki","family":"Sasaki","sequence":"first","affiliation":[{"name":"Graduate School of Information Science, Nara Institute of Science and Technology, Nara 630-0192, Japan"}]},{"given":"Voot","family":"Tangkaratt","sequence":"additional","affiliation":[{"name":"Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan"}]},{"given":"Gang","family":"Niu","sequence":"additional","affiliation":[{"name":"Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-033, Japan"}]},{"given":"Masashi","family":"Sugiyama","sequence":"additional","affiliation":[{"name":"Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan, and Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-033, Japan"}]}],"member":"281","reference":[{"key":"B1","volume-title":"UCI machine learning repository","author":"Bache K.","year":"2013"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144596302644"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1145\/1961189.1961199"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02481097"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1080\/03610920008832598"},{"key":"B6","volume-title":"Local polynomial modelling and its applications","author":"Fan J.","year":"1996"},{"key":"B7","first-page":"73","volume":"5","author":"Fukumizu K.","year":"2004","journal-title":"Journal of Machine Learning Research"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS637"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2013.838167"},{"key":"B10","first-page":"585","volume-title":"Advances in neural information processing systems","volume":"20","author":"Gretton A.","year":"2007"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1015345954"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.2307\/3318636"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1991.10475035"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1992.10476258"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1007\/b98874"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1993.10476348"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44845-8_2"},{"key":"B18","first-page":"1177","author":"Sasaki H.","year":"2016","journal-title":"Proceedings of the 19th International Conference on Artificial Intelligence and Statistics"},{"key":"B19","first-page":"33","author":"Sasaki H.","year":"2015","journal-title":"Proceedings of the 7th Asian Conference on Machine Learning"},{"key":"B20","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4175.001.0001","volume-title":"Learning with kernels: Support vector machines, regularization, optimization, and beyond","author":"Sch\u00f6lkopf B.","year":"2001"},{"key":"B21","author":"Shiino H.","year":"2016","journal-title":"Whitening-free least-squares non-gaussian component analysis"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3324-9"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00407"},{"key":"B24","doi-asserted-by":"publisher","DOI":"10.1162\/neco_a_00986"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1162\/NECO_a_00683"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000352"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.03411"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/neco_a_01035","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T22:15:13Z","timestamp":1719612913000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/30\/2\/477-504\/8346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,2]]}},"alternative-id":["10.1162\/neco_a_01035"],"URL":"https:\/\/doi.org\/10.1162\/neco_a_01035","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2]]}}}