{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T02:49:06Z","timestamp":1781146146243,"version":"3.54.1"},"publisher-location":"Cham","reference-count":44,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319541839","type":"print"},{"value":"9783319541846","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-54184-6_10","type":"book-chapter","created":{"date-parts":[[2017,3,9]],"date-time":"2017-03-09T10:44:25Z","timestamp":1489056265000},"page":"154-170","source":"Crossref","is-referenced-by-count":7,"title":["Variational Gaussian Process Auto-Encoder for Ordinal Prediction of Facial Action Units"],"prefix":"10.1007","author":[{"given":"Stefanos","family":"Eleftheriadis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ognjen","family":"Rudovic","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marc Peter","family":"Deisenroth","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maja","family":"Pantic","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,3,10]]},"reference":[{"key":"10_CR1","doi-asserted-by":"crossref","unstructured":"Bartlett, M., Whitehill, J.: Automated facial expression measurement: recent applications to basic research in human behavior, learning, and education. In: Handbook of Face Perception. Oxford University Press, USA (2010)","DOI":"10.1093\/oxfordhb\/9780199559053.013.0025"},{"key":"10_CR2","unstructured":"Ekman, P., Friesen, W.V., Hager, J.C.: Facial action coding system. UT: A Human Face, Salt Lake City (2002)"},{"key":"10_CR3","doi-asserted-by":"crossref","first-page":"3505","DOI":"10.1098\/rstb.2009.0135","volume":"364","author":"M Pantic","year":"2009","unstructured":"Pantic, M.: Machine analysis of facial behaviour: naturalistic and dynamic behaviour. Philos. Trans. Roy. Soc. B: Biol. Sci. 364, 3505\u20133513 (2009)","journal-title":"Philos. Trans. Roy. Soc. B: Biol. Sci."},{"key":"10_CR4","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1109\/TPAMI.2014.2356192","volume":"37","author":"O Rudovic","year":"2015","unstructured":"Rudovic, O., Pavlovic, V., Pantic, M.: Context-sensitive dynamic ordinal regression for intensity estimation of facial action units. IEEE TPAMI 37, 944\u2013958 (2015)","journal-title":"IEEE TPAMI"},{"key":"10_CR5","doi-asserted-by":"crossref","unstructured":"Mahoor, M.H., Cadavid, S., Messinger, D.S., Cohn, J.F.: A framework for automated measurement of the intensity of non-posed facial action units. In: IEEE CVPR-W, pp. 74\u201380 (2009)","DOI":"10.1109\/CVPRW.2009.5204259"},{"key":"10_CR6","first-page":"151","volume":"4","author":"SM Mavadati","year":"2013","unstructured":"Mavadati, S.M., Mahoor, M.H., Bartlett, K., Trinh, P., Cohn, J.F.: DISFA: a spontaneous facial action intensity database. IEEE TAC 4, 151\u2013160 (2013)","journal-title":"IEEE TAC"},{"key":"10_CR7","doi-asserted-by":"crossref","unstructured":"Ming, Z., Bugeau, A., Rouas, J.L., Shochi, T.: Facial action units intensity estimation by the fusion of features with multi-kernel support vector machine. In: IEEE FG, vol. 6, pp. 1\u20136 (2015)","DOI":"10.1109\/FG.2015.7284870"},{"key":"10_CR8","doi-asserted-by":"crossref","unstructured":"Valstar, M.F., Almaev, T., Girard, J.M., McKeown, G., Mehu, M., Yin, L., Pantic, M., Cohn, J.F.: FERA 2015 - second facial expression recognition and analysis challenge. In: IEEE FG, vol. 6, pp. 1\u20138 (2015)","DOI":"10.1109\/FG.2015.7284874"},{"key":"10_CR9","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1016\/j.imavis.2011.11.008","volume":"30","author":"A Savran","year":"2012","unstructured":"Savran, A., Sankur, B., Bilge, M.T.: Regression-based intensity estimation of facial action units. Image Vis. Comput. 30, 774\u2013784 (2012)","journal-title":"Image Vis. Comput."},{"key":"10_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1007\/978-3-642-33191-6_36","volume-title":"Advances in Visual Computing","author":"S Kaltwang","year":"2012","unstructured":"Kaltwang, S., Rudovic, O., Pantic, M.: Continuous pain intensity estimation from facial expressions. In: Bebis, G., et al. (eds.) ISVC 2012. LNCS, vol. 7432, pp. 368\u2013377. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-33191-6_36"},{"key":"10_CR11","doi-asserted-by":"crossref","unstructured":"Jeni, L.A., Girard, J.M., Cohn, J.F., De La Torre, F.: Continuous AU intensity estimation using localized, sparse facial feature space. In: IEEE FG, pp. 1\u20137 (2013)","DOI":"10.1109\/FG.2013.6553808"},{"key":"10_CR12","doi-asserted-by":"crossref","first-page":"1748","DOI":"10.1109\/TPAMI.2015.2501824","volume":"38","author":"S Kaltwang","year":"2015","unstructured":"Kaltwang, S., Todorovic, S., Pantic, M.: Doubly sparse relevance vector machine for continuous facial behavior estimation. IEEE TPAMI 38, 1748\u20131761 (2015)","journal-title":"IEEE TPAMI"},{"key":"10_CR13","unstructured":"Li, Y., Mavadati, S.M., Mahoor, M.H., Ji, Q.: A unified probabilistic framework for measuring the intensity of spontaneous facial action units. In: IEEE FG (2013)"},{"key":"10_CR14","doi-asserted-by":"crossref","unstructured":"Sandbach, G., Zafeiriou, S., Pantic, M.: Markov random field structures for facial action unit intensity estimation. In: IEEE ICCV-W, pp. 738\u2013745 (2013)","DOI":"10.1109\/ICCVW.2013.101"},{"key":"10_CR15","doi-asserted-by":"crossref","unstructured":"Kaltwang, S., Todorovic, S., Pantic, M.: Latent trees for estimating intensity of facial action units. In: IEEE CVPR, pp. 296\u2013304 (2015)","DOI":"10.1109\/CVPR.2015.7298626"},{"key":"10_CR16","doi-asserted-by":"crossref","unstructured":"Nicolle, J., Bailly, K., Chetouani, M.: Facial action unit intensity prediction via hard multi-task metric learning for kernel regression. In: IEEE FG, pp. 1\u20136 (2015)","DOI":"10.1109\/FG.2015.7284868"},{"key":"10_CR17","first-page":"817","volume":"46","author":"MR Mohammadi","year":"2016","unstructured":"Mohammadi, M.R., Fatemizadeh, E., Mahoor, M.H.: Intensity estimation of spontaneous facial action units based on their sparsity properties. IEEE TCYB 46, 817\u2013826 (2016)","journal-title":"IEEE TCYB"},{"key":"10_CR18","unstructured":"Damianou, A., Ek, C.H., Titsias, M., Lawrence, N.: Manifold relevance determination. In: ICML, pp. 145\u2013152 (2012)"},{"key":"10_CR19","unstructured":"Urtasun, R., Quattoni, A., Lawrence, N., Darrell, T.: Transferring nonlinear representations using Gaussian processes with a shared latent space. Technical report MIT-CSAIL-TR-08-020 (2008)"},{"key":"10_CR20","doi-asserted-by":"crossref","unstructured":"Calandra, R., Peters, J., Rasmussen, C.E., Deisenroth, M.P.: Manifold Gaussian processes for regression. In: IJCNN (2016)","DOI":"10.1109\/IJCNN.2016.7727626"},{"key":"10_CR21","volume-title":"Gaussian Processes for Machine Learning","author":"C Rasmussen","year":"2006","unstructured":"Rasmussen, C., Williams, C.: Gaussian Processes for Machine Learning, vol. 1. MIT Press, Cambridge (2006)"},{"key":"10_CR22","unstructured":"Titsias, M.K., Lawrence, N.D.: Bayesian Gaussian process latent variable model. In: AISTATS, pp. 844\u2013851 (2010)"},{"key":"10_CR23","unstructured":"Dai, Z., Damianou, A., Gonz\u00e1lez, J., Lawrence, N.: Variational auto-encoded deep Gaussian processes. In: ICLR (2016)"},{"key":"10_CR24","doi-asserted-by":"crossref","DOI":"10.1002\/9780470594001","volume-title":"Analysis of Ordinal Categorical Data","author":"A Agresti","year":"2010","unstructured":"Agresti, A.: Analysis of Ordinal Categorical Data. Wiley, Hoboken (2010)"},{"key":"10_CR25","doi-asserted-by":"crossref","unstructured":"Mahoor, M.H., Zhou, M., Veon, K.L., Mavadati, S.M., Cohn, J.F.: Facial action unit recognition with sparse representation. In: IEEE FG, pp. 336\u2013342 (2011)","DOI":"10.1109\/FG.2011.5771420"},{"key":"10_CR26","doi-asserted-by":"crossref","unstructured":"Chu, W.S., Torre, F.D.L., Cohn, J.F.: Selective transfer machine for personalized facial action unit detection. In: IEEE CVPR, pp. 3515\u20133522 (2013)","DOI":"10.1109\/CVPR.2013.451"},{"key":"10_CR27","doi-asserted-by":"crossref","unstructured":"Zhao, K., Chu, W.S., De la Torre, F., Cohn, J.F., Zhang, H.: Joint patch and multi-label learning for facial action unit detection. In: IEEE CVPR (2015)","DOI":"10.1109\/CVPR.2015.7298833"},{"key":"10_CR28","doi-asserted-by":"crossref","unstructured":"Eleftheriadis, S., Rudovic, O., Pantic, M.: Multi-conditional latent variable model for joint facial action unit detection. In: IEEE ICCV, pp. 3792\u20133800 (2015)","DOI":"10.1109\/ICCV.2015.432"},{"key":"10_CR29","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1145\/1970392.1970395","volume":"58","author":"EJ Cand\u00e8s","year":"2011","unstructured":"Cand\u00e8s, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58, 11 (2011)","journal-title":"J. ACM"},{"key":"10_CR30","unstructured":"Kingma, D.P., Welling, M.: Auto-encoding variational Bayes. In: ICLR (2013)"},{"key":"10_CR31","unstructured":"Rezende, D.J., Mohamed, S., Wierstra, D.: Stochastic backpropagation and approximate inference in deep generative models. In: ICML, pp. 1278\u20131286 (2014)"},{"key":"10_CR32","first-page":"1019","volume":"6","author":"W Chu","year":"2005","unstructured":"Chu, W., Ghahramani, Z.: Gaussian processes for ordinal regression. JMLR 6, 1019\u20131041 (2005)","journal-title":"JMLR"},{"key":"10_CR33","unstructured":"Zeiler, M.D.: ADADELTA: an adaptive learning rate method. arXiv preprint arXiv:1212.5701 (2012)"},{"key":"10_CR34","doi-asserted-by":"crossref","unstructured":"Lawrence, N.D., Candela, J.Q.: Local distance preservation in the GP-LVM through back constraints. In: ICML, vol. 148, pp. 513\u2013520 (2006)","DOI":"10.1145\/1143844.1143909"},{"key":"10_CR35","first-page":"1783","volume":"6","author":"N Lawrence","year":"2005","unstructured":"Lawrence, N.: Probabilistic non-linear principal component analysis with Gaussian process latent variable models. JMLR 6, 1783\u20131816 (2005)","journal-title":"JMLR"},{"key":"10_CR36","first-page":"1233","volume":"18","author":"A Shon","year":"2006","unstructured":"Shon, A., Grochow, K., Hertzmann, A., Rao, R.: Learning shared latent structure for image synthesis and robotic imitation. NIPS 18, 1233\u20131240 (2006)","journal-title":"NIPS"},{"key":"10_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/978-3-540-78155-4_12","volume-title":"Machine Learning for Multimodal Interaction","author":"CH Ek","year":"2008","unstructured":"Ek, C.H., Torr, P.H.S., Lawrence, N.D.: Gaussian process latent variable models for human pose estimation. In: Popescu-Belis, A., Renals, S., Bourlard, H. (eds.) MLMI 2007. LNCS, vol. 4892, pp. 132\u2013143. Springer, Heidelberg (2008). doi: 10.1007\/978-3-540-78155-4_12"},{"key":"10_CR38","first-page":"189","volume":"24","author":"S Eleftheriadis","year":"2015","unstructured":"Eleftheriadis, S., Rudovic, O., Pantic, M.: Discriminative shared Gaussian processes for multiview and view-invariant facial expression recognition. IEEE TIP 24, 189\u2013204 (2015)","journal-title":"IEEE TIP"},{"key":"10_CR39","unstructured":"Damianou, A., Lawrence, N.: Semi-described and semi-supervised learning with Gaussian processes. In: UAI (2015)"},{"key":"10_CR40","unstructured":"LeCun, Y., Cortes, C., Burges, C.J.: The MNIST database of handwritten digits (1998)"},{"key":"10_CR41","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1016\/j.imavis.2014.06.002","volume":"32","author":"X Zhang","year":"2014","unstructured":"Zhang, X., Yin, L., Cohn, J.F., Canavan, S., Reale, M., Horowitz, A., Liu, P., Girard, J.M.: BP4D-spontaneous: a high-resolution spontaneous 3D dynamic facial expression database. Image Vis. Comput. 32, 692\u2013706 (2014)","journal-title":"Image Vis. Comput."},{"key":"10_CR42","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1109\/TPAMI.2002.1017623","volume":"24","author":"T Ojala","year":"2002","unstructured":"Ojala, T., Pietikainen, M., Maenpaa, T.: Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE TPAMI 24, 971\u2013987 (2002)","journal-title":"IEEE TPAMI"},{"key":"10_CR43","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1037\/0033-2909.86.2.420","volume":"86","author":"PE Shrout","year":"1979","unstructured":"Shrout, P.E., Fleiss, J.L.: Intraclass correlations: uses in assessing rater reliability. Psychol. Bull. 86, 420 (1979)","journal-title":"Psychol. Bull."},{"key":"10_CR44","unstructured":"Sheth, R., Wang, Y., Khardon, R.: Sparse variational inference for generalized GP models. In: ICML, pp. 1302\u20131311 (2015)"}],"container-title":["Lecture Notes in Computer Science","Computer Vision \u2013 ACCV 2016"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-54184-6_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,19]],"date-time":"2019-09-19T10:42:39Z","timestamp":1568889759000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-54184-6_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319541839","9783319541846"],"references-count":44,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-54184-6_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}