{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T10:35:07Z","timestamp":1785148507931,"version":"3.55.0"},"reference-count":247,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"11","license":[{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001381","name":"Rolls-Royce@NTU Corporate Laboratory, National Research Foundation (NRF) Singapore, through the Corp Lab@University Scheme","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001381","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001475","name":"Data Science and Artificial Intelligence Research Center (DSAIR) and the School of Computer Science and Engineering, Nanyang Technological University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001475","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Neural Netw. Learning Syst."],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1109\/tnnls.2019.2957109","type":"journal-article","created":{"date-parts":[[2020,1,7]],"date-time":"2020-01-07T20:51:43Z","timestamp":1578430303000},"page":"4405-4423","source":"Crossref","is-referenced-by-count":658,"title":["When Gaussian Process Meets Big Data: A Review of Scalable GPs"],"prefix":"10.1109","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1187-5374","authenticated-orcid":false,"given":"Haitao","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4480-169X","authenticated-orcid":false,"given":"Yew-Soon","family":"Ong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaobo","family":"Shen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9444-3763","authenticated-orcid":false,"given":"Jianfei","family":"Cai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref170","first-page":"1459","article-title":"Computationally efficient convolved multiple output Gaussian processes","volume":"12","author":"\u00e1lvarez","year":"2011","journal-title":"J Mach Learn Res"},{"key":"ref172","first-page":"3501","article-title":"Learning stationary time series using Gaussian processes with nonparametric kernels","author":"tobar","year":"2015","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref171","first-page":"2849","article-title":"Convolutional Gaussian processes","author":"van der wilk","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref174","article-title":"Efficient multiscale Gaussian process regression using hierarchical clustering","author":"zhang","year":"2015","journal-title":"arXiv 1511 02258"},{"key":"ref173","doi-asserted-by":"publisher","DOI":"10.1145\/1390156.1390296"},{"key":"ref176","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stw1618"},{"key":"ref175","first-page":"461","article-title":"Variable noise and dimensionality reduction for sparse Gaussian processes","author":"snelson","year":"2006","journal-title":"Proc Conf Uncertainty of Artificial Intelligence"},{"key":"ref178","first-page":"841","article-title":"Variational heteroscedastic Gaussian process regression","author":"l\u00e1zaro-gredilla","year":"2011","journal-title":"Proc Int Conf Int Conf Mach Learn"},{"key":"ref177","first-page":"493","article-title":"Regression with input-dependent noise: A Gaussian process treatment","author":"goldberg","year":"1998","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref168","first-page":"737","article-title":"Multiresolution Gaussian processes","author":"fox","year":"2012","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref169","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2014.914946"},{"key":"ref39","first-page":"1087","article-title":"Inter-domain Gaussian processes for sparse inference using inducing features","author":"l\u00e1zaro-gredilla","year":"2009","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2018.11.002"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/130941912"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2015.1027067"},{"key":"ref31","first-page":"1299","article-title":"GPflow: A Gaussian process library using TensorFlow","volume":"18","author":"matthews","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref30","article-title":"Gaussian process models with parallelization and GPU acceleration","author":"dai","year":"2014","journal-title":"arXiv 1410 4984"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/ICDMW.2017.89"},{"key":"ref36","first-page":"2788","article-title":"Asynchronous distributed variational Gaussian process for regression","author":"peng","year":"2017","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref35","first-page":"569","article-title":"A unifying framework of anytime sparse Gaussian process regression models with stochastic variational inference for big data","author":"hoang","year":"2015","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref34","first-page":"370","article-title":"Deep kernel learning","author":"wilson","year":"2016","journal-title":"Proc Artif Intell Statist"},{"key":"ref181","first-page":"5589","article-title":"Deep Gaussian processes with importance-weighted variational inference","author":"salimbeni","year":"2019","journal-title":"Proceedings 36th Int Conf Mach Learn"},{"key":"ref180","article-title":"Gaussian process regression with heteroscedastic or non-Gaussian residuals","author":"wang","year":"2012","journal-title":"arXiv 1212 6246"},{"key":"ref185","article-title":"Variational inference for uncertainty on the inputs of Gaussian process models","author":"damianou","year":"2014","journal-title":"arXiv 1409 2287"},{"key":"ref184","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2010.2070796"},{"key":"ref183","doi-asserted-by":"publisher","DOI":"10.1214\/15-AOS1390"},{"key":"ref182","first-page":"2385","article-title":"Gaussian process conditional density estimation","author":"dutordoir","year":"2018","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref189","first-page":"207","article-title":"Deep Gaussian processes","author":"damianou","year":"2013","journal-title":"Proc Artif Intell Statist"},{"key":"ref188","first-page":"2472","article-title":"Compressed Gaussian process for manifold regression","volume":"17","author":"guhaniyogi","year":"2016","journal-title":"J Mach Learn Res"},{"key":"ref187","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2010.01501.x"},{"key":"ref186","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.2016.7727626"},{"key":"ref28","first-page":"1","article-title":"Generalized robust Bayesian committee machine for large-scale Gaussian process regression","author":"liu","year":"2018","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-017-9766-2"},{"key":"ref179","article-title":"Large-scale heteroscedastic regression via Gaussian process","author":"liu","year":"2018","journal-title":"arXiv 1811 01179"},{"key":"ref29","first-page":"3257","article-title":"Distributed variational inference in sparse Gaussian process regression and latent variable models","author":"gal","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v072.i01"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-012-9338-y"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2200299"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2010.2093575"},{"key":"ref23","first-page":"881","article-title":"Infinite mixtures of Gaussian process experts","author":"rasmussen","year":"2002","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref26","first-page":"1481","article-title":"Distributed Gaussian processes","author":"deisenroth","year":"2015","journal-title":"Proc Int Conf Int Conf Mach Learn"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1162\/089976602760128018"},{"key":"ref50","first-page":"1936","article-title":"A sparse covariance function for exact Gaussian process inference in large datasets","volume":"9","author":"melkumyan","year":"2009","journal-title":"Proc Int Joint Conf Artif Intell"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-00-01251-5"},{"key":"ref154","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2015.2448083"},{"key":"ref153","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v063.i10","article-title":"Parallelizing Gaussian process calculations in R","volume":"63","author":"paciorek","year":"2015","journal-title":"J Stat Softw"},{"key":"ref156","article-title":"Exact Gaussian processes on a million data points","author":"wang","year":"2019","journal-title":"arXiv 1903 08114"},{"key":"ref155","article-title":"Learning of Gaussian processes in distributed and communication limited systems","author":"tavassolipour","year":"2017","journal-title":"arXiv 1705 02627"},{"key":"ref150","first-page":"4485","article-title":"String and membrane Gaussian processes","volume":"17","author":"samo","year":"2016","journal-title":"J Mach Learn Res"},{"key":"ref152","article-title":"A short note on Gaussian process modeling for large datasets using graphics processing units","author":"franey","year":"2012","journal-title":"arXiv 1203 1269"},{"key":"ref151","first-page":"753","article-title":"Active Markov information-theoretic path planning for robotic environmental sensing","author":"low","year":"2011","journal-title":"Proc 10th Int Conf Auton Agents Multiagent Syst"},{"key":"ref146","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300014908"},{"key":"ref147","article-title":"Hierarchical mixture-of-experts model for large-scale Gaussian process regression","author":"ng","year":"2014","journal-title":"arXiv 1412 3078"},{"key":"ref148","doi-asserted-by":"publisher","DOI":"10.1007\/s10115-017-1084-7"},{"key":"ref149","article-title":"An asymptotic analysis of distributed nonparametric methods","author":"szabo","year":"2017","journal-title":"arXiv 1711 03149"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2007.00633.x"},{"key":"ref58","first-page":"3763","article-title":"EigenGP: Gaussian process models with adaptive eigenfunctions","author":"peng","year":"2015","journal-title":"Proc Int Joint Conf Artif Intell"},{"key":"ref57","first-page":"211","article-title":"Sparse Bayesian learning and the relevance vector machine","volume":"1","author":"tipping","year":"2001","journal-title":"J Mach Learn Res"},{"key":"ref56","first-page":"619","article-title":"Sparse greedy Gaussian process regression","author":"smola","year":"2001","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref55","article-title":"Observations on the nystr&#x00F6;m method for Gaussian process prediction","author":"williams","year":"2002"},{"key":"ref54","first-page":"682","article-title":"Using the Nystr&#x00F6;m method to speed up kernel machines","author":"williams","year":"2001","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref53","first-page":"3977","article-title":"Revisiting the nystr&#x00F6;m method for improved large-scale machine learning","volume":"17","author":"gittens","year":"2016","journal-title":"J Mach Learn Res"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511617539"},{"key":"ref40","first-page":"822","article-title":"Hierarchically-partitioned Gaussian process approximation","author":"lee","year":"2017","journal-title":"Proc Artif Intell Statist"},{"key":"ref167","first-page":"95","article-title":"Hierarchical Gaussian process regression","author":"park","year":"2010","journal-title":"Proc Asian Conf Mach Learn"},{"key":"ref166","first-page":"2213","article-title":"Tree-structured Gaussian process approximations","author":"bui","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref165","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2200694"},{"key":"ref164","first-page":"571","article-title":"Modelling local and global phenomena with sparse Gaussian processes","author":"vanhatalo","year":"2008","journal-title":"Proc 24th Conf Uncertainty Artif Intell"},{"key":"ref163","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3895"},{"key":"ref162","first-page":"3740","article-title":"Multiresolution kernel approximation for Gaussian process regression","author":"ding","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref161","first-page":"2821","article-title":"Parallel Gaussian process regression for big data: Low-rank representation meets Markov approximation","author":"low","year":"2015","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"ref160","first-page":"152","article-title":"Parallel Gaussian process regression with low-rank covariance matrix approximations","author":"chen","year":"2013","journal-title":"Proc Uncertainty Artif Intell"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1038\/nature24270"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"lecun","year":"2015","journal-title":"Nature"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.2113\/gsecongeo.58.8.1246"},{"key":"ref5","author":"rasmussen","year":"2006","journal-title":"Gaussian Processes for Machine Learning"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-017-1739-8"},{"key":"ref159","first-page":"163","article-title":"Decentralized data fusion and active sensing with mobile sensors for modeling and predicting spatiotemporal traffic phenomena","author":"chen","year":"2012","journal-title":"Proc Uncertainty Artif Intell"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012413"},{"key":"ref49","first-page":"643","article-title":"A matching pursuit approach to sparse Gaussian process regression","author":"keerthi","year":"2006","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref157","doi-asserted-by":"publisher","DOI":"10.1145\/1327452.1327492"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1561\/2200000036"},{"key":"ref158","first-page":"7576","article-title":"GPyTorch: Blackbox matrix-matrix Gaussian process inference with GPU acceleration","author":"gardner","year":"2018","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref46","author":"preparata","year":"2012","journal-title":"Computational Geometry An Introduction"},{"key":"ref45","article-title":"On random subsampling of Gaussian process regression: A graphon-based analysis","author":"hayashi","year":"2019","journal-title":"arXiv 1901 09541"},{"key":"ref48","article-title":"Bayesian Gaussian process models: PAC-Bayesian generalisation error bounds and sparse approximations","author":"seeger","year":"2003"},{"key":"ref47","first-page":"625","article-title":"Fast sparse Gaussian process methods: The informative vector machine","author":"herbrich","year":"2003","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref42","first-page":"145","article-title":"Fast allocation of Gaussian process experts","author":"nguyen","year":"2014","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref41","first-page":"524","article-title":"Local and global sparse Gaussian process approximations","author":"snelson","year":"2007","journal-title":"Proc Artif Intell Statist"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/MGRS.2015.2510084"},{"key":"ref43","first-page":"382","article-title":"A distributed variational inference framework for unifying parallel sparse Gaussian process regression models","author":"hoang","year":"2016","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2015.2424873"},{"key":"ref72","article-title":"Variational model selection for sparse Gaussian process regression","author":"titsias","year":"2009"},{"key":"ref71","first-page":"231","article-title":"On sparse variational methods and the Kullback&#x2013;Leibler divergence between stochastic processes","volume":"51","author":"matthews","year":"2016","journal-title":"J Mach Learn Res"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2017.1285773"},{"key":"ref76","first-page":"3649","article-title":"A unifying framework for Gaussian process pseudo-point approximations using power expectation propagation","volume":"18","author":"bui","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref77","article-title":"Adam: A method for stochastic optimization","author":"kingma","year":"2014","journal-title":"arXiv 1412 6980"},{"key":"ref74","first-page":"1","article-title":"Regularized variational sparse Gaussian processes","author":"zhe","year":"2017","journal-title":"Proc NIPS Workshop Approx Inference"},{"key":"ref75","article-title":"Scalable Gaussian process inference using variational methods","author":"de garis matthews","year":"2017"},{"key":"ref78","first-page":"1303","article-title":"Stochastic variational inference","volume":"14","author":"hoffman","year":"2013","journal-title":"J Mach Learn Res"},{"key":"ref79","first-page":"689","article-title":"Natural gradients in practice: Non-conjugate variational inference in Gaussian process models","author":"salimbeni","year":"2018","journal-title":"Proc Artif Intell Statist"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1145\/1102351.1102438"},{"key":"ref62","first-page":"655","article-title":"Improving the Gaussian process sparse spectrum approximation by representing uncertainty in frequency inputs","author":"gal","year":"2015","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref61","first-page":"1865","article-title":"Sparse spectrum Gaussian process regression","volume":"11","author":"l\u00e1zaro-gredilla","year":"2010","journal-title":"J Mach Learn Res"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-015-9600-7"},{"key":"ref64","first-page":"2007","article-title":"A generalized stochastic variational Bayesian hyperparameter learning framework for sparse spectrum Gaussian process regression","author":"hoang","year":"2017","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1162\/089976602317250933"},{"key":"ref66","article-title":"Fast forward selection to speed up sparse Gaussian process regression","author":"seeger","year":"2003","journal-title":"Proc Artif Intell Statist"},{"key":"ref67","first-page":"1257","article-title":"Sparse Gaussian processes using pseudo-inputs","author":"snelson","year":"2006","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref68","article-title":"Flexible and efficient Gaussian process models for machine learning","author":"snelson","year":"2008"},{"key":"ref69","first-page":"1533","article-title":"Understanding probabilistic sparse Gaussian process approximations","author":"bauer","year":"2016","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref197","first-page":"1472","article-title":"Deep Gaussian processes for regression using approximate expectation propagation","author":"bui","year":"2016","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref198","first-page":"4588","article-title":"Doubly stochastic variational inference for deep Gaussian processes","author":"salimbeni","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref199","first-page":"884","article-title":"Random feature expansions for deep Gaussian processes","author":"cutajar","year":"2017","journal-title":"Proc 34th Int Conf Mach Learn"},{"key":"ref193","article-title":"Adversarial examples, uncertainty, and transfer testing robustness in Gaussian process hybrid deep networks","author":"bradshaw","year":"2017","journal-title":"arXiv 1707 02476"},{"key":"ref194","article-title":"Deep Gaussian covariance network","author":"cremanns","year":"2017","journal-title":"arXiv 1710 06202"},{"key":"ref195","article-title":"Improving output uncertainty estimation and generalization in deep learning via neural network Gaussian processes","author":"iwata","year":"2017","journal-title":"arXiv 1707 05922"},{"key":"ref196","article-title":"Variational auto-encoded deep Gaussian processes","author":"dai","year":"2015","journal-title":"arXiv 1511 06455"},{"key":"ref95","doi-asserted-by":"publisher","DOI":"10.1145\/1390156.1390181"},{"key":"ref94","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2013.192"},{"key":"ref190","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0745-0"},{"key":"ref93","article-title":"Scalable inference for structured Gaussian process models","author":"saat\u00e7i","year":"2011"},{"key":"ref191","article-title":"Gaussian process behaviour in wide deep neural networks","author":"matthews","year":"2018","journal-title":"arXiv 1804 11271"},{"key":"ref92","first-page":"2529","article-title":"Preconditioning kernel matrices","author":"cutajar","year":"2016","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref192","first-page":"2850","article-title":"Learning scalable deep kernels with recurrent structure","volume":"18","author":"al-shedivat","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref91","first-page":"1113","article-title":"Automatic online tuning for fast Gaussian summation","author":"morariu","year":"2009","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref90","first-page":"1225","article-title":"Fast Gaussian process regression using KD-trees","author":"shen","year":"2006","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref98","article-title":"Thoughts on massively scalable Gaussian processes","author":"wilson","year":"2015","journal-title":"arXiv 1511 01870"},{"key":"ref99","first-page":"2586","article-title":"Stochastic variational deep kernel learning","author":"wilson","year":"2016","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref96","first-page":"3626","article-title":"Fast kernel learning for multidimensional pattern extrapolation","author":"wilson","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref97","first-page":"4111","article-title":"Constant-time predictive distributions for Gaussian processes","author":"pleiss","year":"2018","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref82","first-page":"5184","article-title":"Variational inference for Gaussian process models with linear complexity","author":"cheng","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref81","first-page":"19","article-title":"Communication efficient distributed machine learning with the parameter server","author":"li","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref84","article-title":"Scalable Gaussian processes with billions of inducing inputs via tensor train decomposition","author":"izmailov","year":"2017","journal-title":"arXiv 1710 07324"},{"key":"ref83","article-title":"Blitzkriging: Kronecker-structured stochastic Gaussian processes","author":"nickson","year":"2015","journal-title":"arXiv 1510 07965"},{"key":"ref80","first-page":"1","article-title":"Distributed delayed proximal gradient methods","volume":"3","author":"li","year":"2013","journal-title":"Proc NIPS Workshop Optim Mach Learn"},{"key":"ref89","article-title":"Variational Fourier features for Gaussian processes","author":"hensman","year":"2016","journal-title":"arXiv 1611 06740"},{"key":"ref85","first-page":"279","article-title":"Variational inference for Mahalanobis distance metrics in Gaussian process regression","author":"aueb","year":"2013","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref86","first-page":"1648","article-title":"MCMC for variationally sparse Gaussian processes","author":"hensman","year":"2015","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref87","article-title":"Stochastic variational inference for Bayesian sparse Gaussian process regression","author":"yu","year":"2017","journal-title":"arXiv 1711 00221"},{"key":"ref88","first-page":"1302","article-title":"Sparse variational inference for generalized GP models","author":"sheth","year":"2015","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref200","first-page":"7506","article-title":"Inference in deep Gaussian processes using stochastic gradient Hamiltonian Monte Carlo","author":"havasi","year":"2018","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref101","article-title":"Product kernel interpolation for scalable Gaussian processes","author":"gardner","year":"2018","journal-title":"arXiv 1802 08903"},{"key":"ref100","first-page":"1416","article-title":"Scalable Gaussian processes with grid-structured eigenfunctions (GP-GRIEF)","author":"evans","year":"2017","journal-title":"Proc NIPS Workshop Adv Approx Bayesian Inference"},{"key":"ref209","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2019.2945133"},{"key":"ref203","first-page":"1812","article-title":"Deep learning with differential Gaussian process flows","author":"hegde","year":"2019","journal-title":"Proc Int Conf Artif Intell Statist"},{"key":"ref204","first-page":"1425","article-title":"Variational inference for latent variables and uncertain inputs in Gaussian processes","volume":"17","author":"damianou","year":"2016","journal-title":"J Mach Learn Res"},{"key":"ref201","first-page":"844","article-title":"Bayesian Gaussian process latent variable model","author":"titsias","year":"2010","journal-title":"Proc 13th Int Conf Artif Intell Statist"},{"key":"ref202","article-title":"Deep Gaussian processes with convolutional kernels","author":"kumar","year":"2018","journal-title":"arXiv 1806 01655"},{"key":"ref207","first-page":"4134","article-title":"Variational dependent multi-output Gaussian process dynamical systems","volume":"17","author":"zhao","year":"2016","journal-title":"J Mach Learn Res"},{"key":"ref208","first-page":"88","article-title":"Approximate inference in related multi-output Gaussian process regression","author":"chiplunkar","year":"2016","journal-title":"Proc Int Conf Pattern Recognit Appl Methods"},{"key":"ref205","first-page":"153","article-title":"Multi-task Gaussian process prediction","author":"bonilla","year":"2008","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref206","first-page":"643","article-title":"Collaborative multi-output Gaussian processes","author":"nguyen","year":"2014","journal-title":"Proc 13th Conf Uncertainty Artif Intell"},{"key":"ref211","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2014.03.004"},{"key":"ref210","doi-asserted-by":"publisher","DOI":"10.1109\/EAIS.2014.6867476"},{"key":"ref212","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2017.35"},{"key":"ref213","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2015.12.212"},{"key":"ref214","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacsc.2017.09.001"},{"key":"ref215","first-page":"4410","article-title":"Incremental variational sparse Gaussian process regression","author":"cheng","year":"2016","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref216","first-page":"3299","article-title":"Streaming sparse Gaussian process approximations","author":"bui","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref217","first-page":"1193","article-title":"Local Gaussian process regression for real time online model learning","author":"nguyen-tuong","year":"2009","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref218","first-page":"2585","article-title":"GP-localize: Persistent mobile robot localization using online sparse Gaussian process observation model","author":"xu","year":"2014","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"ref219","first-page":"1","article-title":"Online variational Bayesian inference: Algorithms for sparse Gaussian processes and theoretical bounds","author":"nguyen","year":"2017","journal-title":"Proceedings of ICML Time Series Workshop"},{"key":"ref220","doi-asserted-by":"publisher","DOI":"10.1080\/13873950500068567"},{"key":"ref222","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24834-9_21"},{"key":"ref221","first-page":"3680","article-title":"Variational Gaussian process state-space models","author":"frigola","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref229","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2019.01.005"},{"key":"ref228","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2017.06.010"},{"key":"ref227","first-page":"213","article-title":"Computationally efficient Bayesian learning of Gaussian process state space models","author":"svensson","year":"2016","journal-title":"Proc Artif Intell Statist"},{"key":"ref226","first-page":"3156","article-title":"Bayesian inference and learning in Gaussian process state-space models with particle MCMC","author":"frigola","year":"2013","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref225","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2013.6760734"},{"key":"ref224","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08985-0_14"},{"key":"ref223","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2010.10.010"},{"key":"ref127","first-page":"57","article-title":"Bayesian hierarchical mixtures of experts","author":"bishop","year":"2002","journal-title":"Proc 19th Conf Uncertainty Artif Intell"},{"key":"ref126","doi-asserted-by":"publisher","DOI":"10.1016\/j.artmed.2007.06.001"},{"key":"ref125","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1994.6.2.181"},{"key":"ref124","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(99)00043-X"},{"key":"ref129","first-page":"654","article-title":"Mixtures of Gaussian processes","author":"tresp","year":"2001","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref128","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.05.044"},{"key":"ref130","first-page":"883","article-title":"An alternative infinite mixture of Gaussian process experts","author":"meeds","year":"2006","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref133","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2016.7472143"},{"key":"ref134","first-page":"1897","article-title":"Variational mixture of Gaussian process experts","author":"yuan","year":"2009","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref131","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-21090-7_20"},{"key":"ref132","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-09339-0_7"},{"key":"ref232","doi-asserted-by":"crossref","first-page":"1948","DOI":"10.1109\/TPAMI.2006.238","article-title":"Bayesian Gaussian process classification with the EM-EP algorithm","volume":"28","author":"kim","year":"2006","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"ref233","first-page":"1745","article-title":"Variational multinomial logit Gaussian process","volume":"13","author":"chai","year":"2012","journal-title":"J Mach Learn Res"},{"key":"ref230","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1735"},{"key":"ref231","first-page":"2035","article-title":"Approximations for binary Gaussian process classification","volume":"9","author":"nickisch","year":"2008","journal-title":"J Mach Learn Res"},{"key":"ref239","first-page":"168","article-title":"Scalable Gaussian process classification via expectation propagation","author":"hern\u00e1ndez-lobato","year":"2016","journal-title":"Proc Artif Intell Statist"},{"key":"ref238","first-page":"351","article-title":"Scalable variational Gaussian process classification","author":"hensman","year":"2015","journal-title":"Proc Artif Intell Statist"},{"key":"ref235","doi-asserted-by":"publisher","DOI":"10.1007\/s00138-012-0480-y"},{"key":"ref234","first-page":"6997","article-title":"Augment and reduce: Stochastic inference for large Categorical distributions","volume":"10","author":"ruiz","year":"2018","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref237","first-page":"1057","article-title":"The generalized FITC approximation","author":"naish-guzman","year":"2008","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref236","first-page":"6008","article-title":"Dirichlet-based Gaussian processes for large-scale calibrated classification","author":"milios","year":"2018","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref136","first-page":"1346","article-title":"Nonparametric mixture of Gaussian processes with constraints","author":"ross","year":"2013","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref135","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2011.10.004"},{"key":"ref138","doi-asserted-by":"publisher","DOI":"10.1163\/016918609X12529286896877"},{"key":"ref137","article-title":"Combining predictors: Meta machine learning methods and bias\/variance & ambiguity decompositions","author":"hansen","year":"2000"},{"key":"ref139","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2510000"},{"key":"ref140","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2013.868084"},{"key":"ref141","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-25393-0_38"},{"key":"ref142","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2217986"},{"key":"ref143","article-title":"Generalized product of experts for automatic and principled fusion of Gaussian process predictions","author":"cao","year":"2014","journal-title":"arXiv 1410 7827"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.03.043"},{"key":"ref144","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2008.09.002"},{"key":"ref1","first-page":"282","article-title":"Gaussian processes for big data","author":"hensman","year":"2013","journal-title":"Proc Conf Uncertainty of Artificial Intelligence"},{"key":"ref145","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40728-4_3"},{"key":"ref241","first-page":"5417","article-title":"Efficient Gaussian process classification using P&#x00F3;lya-Gamma data augmentation","author":"wenzel","year":"2018","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref242","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2013.829001"},{"key":"ref243","first-page":"1","article-title":"Scalable multi-class Gaussian process classification via data augmentation","author":"galy-fajou","year":"2018","journal-title":"Proc NIPS Workshop Approx Inference"},{"key":"ref244","article-title":"Scalable Gaussian process classification with additive noise for various likelihoods","author":"liu","year":"2019","journal-title":"arXiv preprint arXiv 1909 01771"},{"key":"ref240","first-page":"3550","article-title":"Scalable multi-class Gaussian process classification using expectation propagation","author":"villacampa-calvo","year":"2017","journal-title":"Proc 34th Int Conf Mach Learn"},{"key":"ref247","first-page":"607","article-title":"Fast Kronecker inference in Gaussian processes with non-Gaussian likelihoods","author":"flaxman","year":"2015","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref246","first-page":"972","article-title":"Incremental local Gaussian regression","author":"meier","year":"2014","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref245","first-page":"1697","article-title":"Domain decomposition approach for fast Gaussian process regression of large spatial data sets","volume":"12","author":"park","year":"2011","journal-title":"J Mach Learn Res"},{"key":"ref109","doi-asserted-by":"publisher","DOI":"10.1002\/rob.20309"},{"key":"ref108","doi-asserted-by":"publisher","DOI":"10.1002\/wics.1383"},{"key":"ref107","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000002014"},{"key":"ref106","doi-asserted-by":"publisher","DOI":"10.1080\/0740817X.2013.849833"},{"key":"ref105","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.02.032"},{"key":"ref104","first-page":"444","article-title":"Sparse representation for Gaussian process models","author":"csat\u00f3","year":"2001","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref103","first-page":"862","article-title":"Rates of convergence for sparse variational Gaussian process regression","author":"burt","year":"2019","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref102","first-page":"6327","article-title":"Scalable log determinants for Gaussian process kernel learning","author":"dong","year":"2017","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref111","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9473(01)00073-1"},{"key":"ref112","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2008.4587360"},{"key":"ref110","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2013.841584"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2017.12.034"},{"key":"ref11","first-page":"1783","article-title":"Probabilistic non-linear principal component analysis with Gaussian process latent variable models","volume":"6","author":"lawrence","year":"2005","journal-title":"J Mach Learn Res"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2015.2494218"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2015.2388958"},{"key":"ref14","first-page":"333","article-title":"A framework for evaluating approximation methods for Gaussian process regression","volume":"14","author":"chalupka","year":"2013","journal-title":"J Mach Learn Res"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.2001.2056"},{"key":"ref16","first-page":"1939","article-title":"A unifying view of sparse approximate Gaussian process regression","volume":"6","author":"qui\u00f1onero-candela","year":"2005","journal-title":"J Mach Learn Res"},{"key":"ref118","article-title":"Patchwork Kriging for large-scale Gaussian process regression","author":"park","year":"2017","journal-title":"arXiv 1701 06655"},{"key":"ref17","first-page":"567","article-title":"Variational learning of inducing variables in sparse Gaussian processes","author":"titsias","year":"2009","journal-title":"Proc Artif Intell Statist"},{"key":"ref117","first-page":"1","article-title":"Efficient computation of Gaussian process regression for large spatial data sets by patching local Gaussian processes","volume":"17","author":"park","year":"2016","journal-title":"J Mach Learn Res"},{"key":"ref18","first-page":"1775","article-title":"Kernel interpolation for scalable structured Gaussian processes (KISS-GP)","author":"wilson","year":"2015","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1198\/016214508000000689"},{"key":"ref119","doi-asserted-by":"publisher","DOI":"10.1145\/2379776.2379786"},{"key":"ref114","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-008-9116-8"},{"key":"ref113","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2015.1044091"},{"key":"ref116","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2014.914442"},{"key":"ref115","doi-asserted-by":"publisher","DOI":"10.1198\/TECH.2009.0015"},{"key":"ref120","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1991.3.1.79"},{"key":"ref121","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.05.022"},{"key":"ref122","first-page":"633","article-title":"An alternative model for mixtures of experts","author":"xu","year":"1995","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref123","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.01.009"}],"container-title":["IEEE Transactions on Neural Networks and Learning Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/5962385\/9244673\/08951257.pdf?arnumber=8951257","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T17:19:56Z","timestamp":1651079996000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8951257\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11]]},"references-count":247,"journal-issue":{"issue":"11"},"URL":"https:\/\/doi.org\/10.1109\/tnnls.2019.2957109","relation":{},"ISSN":["2162-237X","2162-2388"],"issn-type":[{"value":"2162-237X","type":"print"},{"value":"2162-2388","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11]]}}}