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The proposed method provides computationally efficient estimation for the derivatives of any order on multidimensional data with a hyperparameter tuning method and achieves the optimal parametric convergence rate. We further discuss an extension of the proposed method by applying regularized multitask learning and a general framework for density derivative estimation based on Bregman divergences. Applications of the proposed method to nonparametric Kullback-Leibler divergence approximation and bandwidth matrix selection in kernel density estimation are also explored.<\/jats:p>","DOI":"10.1162\/neco_a_00835","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T20:41:15Z","timestamp":1462308075000},"page":"1101-1140","source":"Crossref","is-referenced-by-count":9,"title":["Direct Density Derivative Estimation"],"prefix":"10.1162","volume":"28","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":"Yung-Kyun","family":"Noh","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea"}]},{"given":"Gang","family":"Niu","sequence":"additional","affiliation":[{"name":"Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan"}]},{"given":"Masashi","family":"Sugiyama","sequence":"additional","affiliation":[{"name":"Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan"}]}],"member":"281","reference":[{"key":"B1","first-page":"41","volume-title":"Advances in neural information processing systems","author":"Argyriou A.","year":"2007"},{"key":"B2","author":"Bache K.","year":"2013","journal-title":"UCI machine learning repository"},{"key":"B3","first-page":"1705","volume":"6","author":"Banerjee A.","year":"2005","journal-title":"Journal of Machine Learning Research"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.3.549"},{"issue":"4","key":"B5","first-page":"373","volume":"29","author":"Bhattacharya P.","year":"1967","journal-title":"Sankhy\u0101: The Indian Journal of Statistics, Series A"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144596302644"},{"key":"B7","first-page":"95","author":"Bontempi G.","year":"2010","journal-title":"Proceedings of the 27th International Conference on Machine Learning"},{"key":"B8","first-page":"1455","volume":"15","author":"Boumal N.","year":"2014","journal-title":"Journal of Machine Learning Research"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/71.2.353"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(67)90040-7"},{"key":"B11","first-page":"49","author":"Brown G.","year":"2009","journal-title":"Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007379606734"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1007\/s11749-009-0168-4"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.5705\/ss.2011.036a"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1214\/13-EJS781"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1109\/34.400568"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1109\/34.1000236"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02481097"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v021.i07"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9469.2005.00445.x"},{"key":"B21","first-page":"109","author":"Evgeniou T.","year":"2004","journal-title":"Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1158\/0008-5472.CAN-04-0452"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1975.1055330"},{"key":"B24","first-page":"417","author":"Garcia-Garcia D.","year":"2011","journal-title":"Proceedings of 28th International Conference on Machine Learning"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1007\/BF01205233"},{"issue":"1","key":"B26","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1111\/j.2517-6161.1990.tb01783.x","volume":"52","author":"Hardle W.","year":"1990","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2012.07.006"},{"issue":"4","key":"B28","first-page":"337","volume":"19","author":"Jones M.","year":"1992","journal-title":"Scandinavian Journal of Statistics"},{"key":"B29","first-page":"1391","volume":"10","author":"Kanamori T.","year":"2009","journal-title":"Journal of Machine Learning Research"},{"key":"B30","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2163380"},{"key":"B31","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2009.188"},{"key":"B32","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2013.01.012"},{"key":"B33","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2068870"},{"key":"B34","first-page":"669","author":"Noh Y. 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