{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:55:42Z","timestamp":1740149742620,"version":"3.37.3"},"reference-count":45,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,9,21]],"date-time":"2018-09-21T00:00:00Z","timestamp":1537488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["DFG-IRTG 1901 \u2019The Brain in Action\u2019, DFG-SFB-TRR 135 project C06"],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"We describe a sparse, variational posterior approximation to the Coupled Gaussian Process Dynamical Model (CGPDM), which is a latent space coupled dynamical model in discrete time. The purpose of the approximation is threefold: first, to reduce training time of the model; second, to enable modular re-use of learned dynamics; and, third, to store these learned dynamics compactly. Our target applications here are human movement primitive (MP) models, where an MP is a reusable spatiotemporal component, or \u201cmodule\u201d of a human full-body movement. Besides re-usability of learned MPs, compactness is crucial, to allow for the storage of a large library of movements. We first derive the variational approximation, illustrate it on toy data, test its predictions against a range of other MP models and finally compare movements produced by the model against human perceptual expectations. We show that the variational CGPDM outperforms several other MP models on movement trajectory prediction. Furthermore, human observers find its movements nearly indistinguishable from replays of natural movement recordings for a very compact parameterization of the approximation.<\/jats:p>","DOI":"10.3390\/e20100724","type":"journal-article","created":{"date-parts":[[2018,9,21]],"date-time":"2018-09-21T15:00:25Z","timestamp":1537542025000},"page":"724","source":"Crossref","is-referenced-by-count":3,"title":["Making the Coupled Gaussian Process Dynamical Model Modular and Scalable with Variational Approximations"],"prefix":"10.3390","volume":"20","author":[{"given":"Dmytro","family":"Velychko","sequence":"first","affiliation":[{"name":"Department of Psychology, University of Marburg, Gutenbergstr. 18, 35032 Marburg, Germany"}]},{"given":"Benjamin","family":"Knopp","sequence":"additional","affiliation":[{"name":"Department of Psychology, University of Marburg, Gutenbergstr. 18, 35032 Marburg, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9756-9655","authenticated-orcid":false,"given":"Dominik","family":"Endres","sequence":"additional","affiliation":[{"name":"Department of Psychology, University of Marburg, Gutenbergstr. 18, 35032 Marburg, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.brainresrev.2007.08.004","article-title":"Combining modules for movement","volume":"57","author":"Bizzi","year":"2008","journal-title":"Brain Res. 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