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Linear correlations are usually completely removed by ICA and related methods so they can only be analyzed by developing new methods that explicitly allow for linearly correlated components. In this article, we propose a probabilistic model of linear nongaussian components that are allowed to have both linear and energy correlations. The precision matrix of the linear components is assumed to be randomly generated by a higher-order process and explicitly parameterized by a parameter matrix. The estimation of the parameter matrix is shown to be particularly simple because using score-matching (Hyv\u00e4rinen, 2005 ), the objective function is a quadratic form. Using simulations with artificial data, we demonstrate that the proposed method improves the identifiability of nongaussian components by simultaneously learning their correlation structure. Applications on simulated complex cells with natural image input, as well as spectrograms of natural audio data, show that the method finds new kinds of dependencies between the components.<\/jats:p>","DOI":"10.1162\/neco_a_01006","type":"journal-article","created":{"date-parts":[[2017,8,4]],"date-time":"2017-08-04T17:45:22Z","timestamp":1501868722000},"page":"2887-2924","source":"Crossref","is-referenced-by-count":0,"title":["Simultaneous Estimation of Nongaussian Components and Their Correlation Structure"],"prefix":"10.1162","volume":"29","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":"Michael U.","family":"Gutmann","sequence":"additional","affiliation":[{"name":"School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, U.K."}]},{"given":"Hayaru","family":"Shouno","sequence":"additional","affiliation":[{"name":"Graduate School of Informatics and Engineering, University of Electro-Communications, Tokyo 182-8585, Japan"}]},{"given":"Aapo","family":"Hyv\u00e4rinen","sequence":"additional","affiliation":[{"name":"Helsinki Institute for Information Technology, University of Helsinki, Helsinki 00560, Finland, and Gatsby Computational Neuroscience Unit, University College London, London W1T 4JG, U.K."}]}],"member":"281","reference":[{"key":"B1","first-page":"757","volume-title":"Advances in neural information processing systems, 8","author":"Amari S.","year":"1996"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1162\/jmlr.2003.4.7-8.1205"},{"key":"B3","author":"Ball\u00e9 J.","year":"2015","journal-title":"Density modeling of images using a generalized normalization transformation"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-79452-3"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2002.804287"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0619-4"},{"issue":"107","key":"B7","volume":"7","author":"Campi C.","year":"2013","journal-title":"Frontiers in Neuroscience"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.1998.681443"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002405"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(94)90029-9"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxm045"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2008.07.032"},{"key":"B13","first-page":"283","volume-title":"Proc. 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