{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T05:21:48Z","timestamp":1775280108847,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T00:00:00Z","timestamp":1698364800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T00:00:00Z","timestamp":1698364800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003032","name":"Association Nationale de la Recherche et de la Technologie","doi-asserted-by":"publisher","award":["2021\/1284"],"award-info":[{"award-number":["2021\/1284"]}],"id":[{"id":"10.13039\/501100003032","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s00180-023-01424-7","type":"journal-article","created":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T11:03:21Z","timestamp":1698404601000},"page":"3049-3071","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Combination of optimization-free kriging models for high-dimensional problems"],"prefix":"10.1007","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8318-302X","authenticated-orcid":false,"given":"Tanguy","family":"Appriou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Didier","family":"Rulli\u00e8re","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Gaudrie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,27]]},"reference":[{"issue":"3","key":"1424_CR1","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s00158-008-0230-y","volume":"37","author":"E Acar","year":"2009","unstructured":"Acar E, Rais-Rohani M (2009) Ensemble of metamodels with optimized weight factors. Struct Multidiscip Optim 37(3):279\u2013294","journal-title":"Struct Multidiscip Optim"},{"key":"1424_CR2","doi-asserted-by":"crossref","unstructured":"Aggarwal CC, Hinneburg A, Keim DA (2001) On the surprising behavior of distance metrics in high dimensional space. In: International conference on database theory, Springer, pp 420\u2013434","DOI":"10.1007\/3-540-44503-X_27"},{"key":"1424_CR3","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.csda.2013.03.016","volume":"66","author":"F Bachoc","year":"2013","unstructured":"Bachoc F (2013) Cross validation and maximum likelihood estimations of hyper-parameters of gaussian processes with model misspecification. Comput Stat Data Anal 66:55\u201369","journal-title":"Comput Stat Data Anal"},{"issue":"3731","key":"1424_CR4","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1126\/science.153.3731.34","volume":"153","author":"R Bellman","year":"1966","unstructured":"Bellman R (1966) Dynamic programming. Science 153(3731):34\u201337","journal-title":"Science"},{"key":"1424_CR5","unstructured":"Binois M, Wycoff N (2021) A survey on high-dimensional gaussian process modeling with application to bayesian optimization. arXiv preprint arXiv:2111.05040"},{"issue":"5","key":"1424_CR6","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1007\/s00158-015-1395-9","volume":"53","author":"MA Bouhlel","year":"2016","unstructured":"Bouhlel MA, Bartoli N, Otsmane A et al (2016) Improving kriging surrogates of high-dimensional design models by partial least squares dimension reduction. Struct Multidiscip Optim 53(5):935\u2013952","journal-title":"Struct Multidiscip Optim"},{"issue":"1","key":"1424_CR7","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s00265-010-1029-6","volume":"65","author":"KP Burnham","year":"2011","unstructured":"Burnham KP, Anderson DR, Huyvaert KP (2011) Aic model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons. Behav Ecol Sociobiol 65(1):23\u201335","journal-title":"Behav Ecol Sociobiol"},{"key":"1424_CR8","unstructured":"Cao Y, Fleet DJ (2014) Generalized product of experts for automatic and principled fusion of gaussian process predictions. arXiv preprint arXiv:1410.7827"},{"key":"1424_CR9","doi-asserted-by":"crossref","unstructured":"Constantine PG (2015) Active subspaces: Emerging ideas for dimension reduction in parameter studies. SIAM","DOI":"10.1137\/1.9781611973860"},{"key":"1424_CR10","doi-asserted-by":"publisher","DOI":"10.1002\/9781119115151","volume-title":"Statistics for spatial data","author":"N Cressie","year":"1993","unstructured":"Cressie N (1993) Statistics for spatial data. Wiley, Amsterdam"},{"key":"1424_CR11","unstructured":"Deisenroth M, Ng JW (2015) Distributed gaussian processes. In: International Conference on Machine Learning, PMLR, pp 1481\u20131490"},{"key":"1424_CR12","doi-asserted-by":"crossref","unstructured":"Durrande N, Ginsbourger D, Roustant O (2012) Additive Covariance kernels for high-dimensional Gaussian Process modeling. Annales de la Facult\u00e9 des sciences de Toulouse : Math\u00e9matiques Ser. 6, 21(3):481\u2013499","DOI":"10.5802\/afst.1342"},{"issue":"6","key":"1424_CR13","doi-asserted-by":"publisher","first-page":"2343","DOI":"10.1007\/s00158-019-02458-6","volume":"61","author":"D Gaudrie","year":"2020","unstructured":"Gaudrie D, Le Riche R, Picheny V et al (2020) Modeling and optimization with gaussian processes in reduced eigenbases. Struct Multidiscip Optim 61(6):2343\u20132361","journal-title":"Struct Multidiscip Optim"},{"key":"1424_CR14","doi-asserted-by":"crossref","unstructured":"Gelman A, Carlin JB, Stern HS, et\u00a0al (1995) Bayesian data analysis. Chapman and Hall\/CRC","DOI":"10.1201\/9780429258411"},{"key":"1424_CR15","unstructured":"Ginsbourger D, Sch\u00e4rer C (2021) Fast calculation of gaussian process multiple-fold cross-validation residuals and their covariances. arXiv preprint arXiv:2101.03108"},{"issue":"6","key":"1424_CR16","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1002\/qre.945","volume":"24","author":"D Ginsbourger","year":"2008","unstructured":"Ginsbourger D, Helbert C, Carraro L (2008) Discrete mixtures of kernels for kriging-based optimization. Qual Reliab Eng Int 24(6):681\u2013691","journal-title":"Qual Reliab Eng Int"},{"issue":"2","key":"1424_CR17","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1002\/asmb.741","volume":"25","author":"D Ginsbourger","year":"2009","unstructured":"Ginsbourger D, Dupuy D, Badea A et al (2009) A note on the choice and the estimation of kriging models for the analysis of deterministic computer experiments. Appl Stoch Models Bus Ind 25(2):115\u2013131","journal-title":"Appl Stoch Models Bus Ind"},{"issue":"3","key":"1424_CR18","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s00158-006-0051-9","volume":"33","author":"T Goel","year":"2007","unstructured":"Goel T, Haftka RT, Shyy W et al (2007) Ensemble of surrogates. Struct Multidiscip Optim 33(3):199\u2013216","journal-title":"Struct Multidiscip Optim"},{"key":"1424_CR19","unstructured":"Hensman J, Fusi N, Lawrence ND (2013) Gaussian processes for big data. arXiv preprint arXiv:1309.6835"},{"issue":"8","key":"1424_CR20","doi-asserted-by":"publisher","first-page":"1771","DOI":"10.1162\/089976602760128018","volume":"14","author":"GE Hinton","year":"2002","unstructured":"Hinton GE (2002) Training products of experts by minimizing contrastive divergence. Neural comput 14(8):1771\u20131800","journal-title":"Neural comput"},{"issue":"4","key":"1424_CR21","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1214\/ss\/1009212519","volume":"14","author":"JA Hoeting","year":"1999","unstructured":"Hoeting JA, Madigan D, Raftery AE et al (1999) Bayesian model averaging: a tutorial (with comments by m. clyde, david draper and ei george, and a rejoinder by the authors. Stat Sci 14(4):382\u2013417","journal-title":"Stat Sci"},{"issue":"4","key":"1424_CR22","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1023\/A:1012771025575","volume":"21","author":"DR Jones","year":"2001","unstructured":"Jones DR (2001) A taxonomy of global optimization methods based on response surfaces. J Global Optim 21(4):345\u2013383","journal-title":"J Global Optim"},{"issue":"4","key":"1424_CR23","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1023\/A:1008306431147","volume":"13","author":"DR Jones","year":"1998","unstructured":"Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Global Optim 13(4):455\u2013492","journal-title":"J Global Optim"},{"issue":"6","key":"1424_CR24","first-page":"119","volume":"52","author":"DG Krige","year":"1951","unstructured":"Krige DG (1951) A statistical approach to some basic mine valuation problems on the witwatersrand. J Southern Afr Instit Min Metall 52(6):119\u2013139","journal-title":"J Southern Afr Instit Min Metall"},{"issue":"11","key":"1424_CR25","doi-asserted-by":"publisher","first-page":"4405","DOI":"10.1109\/TNNLS.2019.2957109","volume":"31","author":"H Liu","year":"2020","unstructured":"Liu H, Ong YS, Shen X et al (2020) When gaussian process meets big data: a review of scalable gps. IEEE Trans Neural Netw Learn Syst 31(11):4405\u20134423","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"8","key":"1424_CR26","doi-asserted-by":"publisher","first-page":"1246","DOI":"10.2113\/gsecongeo.58.8.1246","volume":"58","author":"G Matheron","year":"1963","unstructured":"Matheron G (1963) Principles of geostatistics. Econ Geol 58(8):1246\u20131266","journal-title":"Econ Geol"},{"key":"1424_CR27","unstructured":"Mohammadi H, Riche RL, Touboul E (2016) Small ensembles of kriging models for optimization. arXiv preprint arXiv:1603.02638"},{"key":"1424_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.17535\/crorr.2018.0001","volume":"9","author":"H Mohammadi","year":"2018","unstructured":"Mohammadi H, Le Riche R, Bay X et al (2018) An analysis of covariance parameters in gaussian process-based optimization. Croat Operat Res Rev 9:1\u201310","journal-title":"Croat Operat Res Rev"},{"key":"1424_CR29","doi-asserted-by":"crossref","unstructured":"Mohammed RO, Cawley GC (2017) Over-fitting in model selection with gaussian process regression. In: International conference on machine learning and data mining in pattern recognition, Springer, pp 192\u2013205","DOI":"10.1007\/978-3-319-62416-7_14"},{"issue":"5","key":"1424_CR30","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1021\/ci7000633","volume":"47","author":"O Obrezanova","year":"2007","unstructured":"Obrezanova O, Cs\u00e1nyi G, Gola JM et al (2007) Gaussian processes: a method for automatic qsar modeling of adme properties. J Chem Inf Model 47(5):1847\u20131857","journal-title":"J Chem Inf Model"},{"issue":"6","key":"1424_CR31","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.1007\/s00158-017-1867-1","volume":"57","author":"PS Palar","year":"2018","unstructured":"Palar PS, Shimoyama K (2018) On efficient global optimization via universal kriging surrogate models. Struct Multidiscip Optim 57(6):2377\u20132397","journal-title":"Struct Multidiscip Optim"},{"issue":"3","key":"1424_CR32","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1080\/00401706.2016.1214179","volume":"59","author":"L Pronzato","year":"2017","unstructured":"Pronzato L, Rendas MJ (2017) Bayesian local kriging. Technometrics 59(3):293\u2013304","journal-title":"Technometrics"},{"key":"1424_CR33","first-page":"1939","volume":"6","author":"J Quinonero-Candela","year":"2005","unstructured":"Quinonero-Candela J, Rasmussen CE (2005) A unifying view of sparse approximate gaussian process regression. J Mach Learn Res 6:1939\u20131959","journal-title":"J Mach Learn Res"},{"key":"1424_CR34","unstructured":"Rasmussen C, Ghahramani Z (2001) Infinite mixtures of gaussian process experts. Adv Neural Inf Process Syst 14"},{"key":"1424_CR35","volume-title":"Gaussian processes for machine learning","author":"CE Rasmussen","year":"2006","unstructured":"Rasmussen CE, Williams CK (2006) Gaussian processes for machine learning. MIT press Cambridge, MA"},{"key":"1424_CR36","unstructured":"Richet Y (2018) Cookbook: lower bounds for kriging maximum likelihood estimation (mle). https:\/\/dicekrigingclub.github.io\/www\/r\/jekyll\/2018\/05\/21\/KrigingMLELowerBound.html, accessed: 2022-09-21"},{"key":"1424_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v051.i01","volume":"51","author":"O Roustant","year":"2012","unstructured":"Roustant O, Ginsbourger D, Deville Y (2012) Dicekriging, diceoptim: two r packages for the analysis of computer experiments by kriging-based metamodeling and optimization. J Stat Softw 51:1\u201355","journal-title":"J Stat Softw"},{"issue":"4","key":"1424_CR38","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1007\/s11222-017-9766-2","volume":"28","author":"D Rulli\u00e8re","year":"2018","unstructured":"Rulli\u00e8re D, Durrande N, Bachoc F et al (2018) Nested kriging predictions for datasets with a large number of observations. Stat Comput 28(4):849\u2013867","journal-title":"Stat Comput"},{"issue":"4","key":"1424_CR39","first-page":"409","volume":"4","author":"J Sacks","year":"1989","unstructured":"Sacks J, Welch WJ, Mitchell TJ et al (1989) Design and analysis of computer experiments. Stat Sci 4(4):409\u2013423","journal-title":"Stat Sci"},{"key":"1424_CR40","volume-title":"Global sensitivity analysis: the primer","author":"A Saltelli","year":"2008","unstructured":"Saltelli A, Ratto M, Andres T et al (2008) Global sensitivity analysis: the primer. Wiley, Amsterdam"},{"key":"1424_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3799-8","volume-title":"The design and analysis of computer experiments,","author":"TJ Santner","year":"2003","unstructured":"Santner TJ, Williams BJ, Notz WI et al (2003) The design and analysis of computer experiments, vol 1. Springer, Berlin"},{"issue":"2","key":"1424_CR42","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s00158-009-0420-2","volume":"41","author":"S Shan","year":"2010","unstructured":"Shan S, Wang GG (2010) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multidiscip Optim 41(2):219\u2013241","journal-title":"Struct Multidiscip Optim"},{"key":"1424_CR43","volume-title":"Engineering design via surrogate modelling: a practical guide","author":"A Sobester","year":"2008","unstructured":"Sobester A, Forrester A, Keane A (2008) Engineering design via surrogate modelling: a practical guide. Wiley, Amsterdam"},{"key":"1424_CR44","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1494-6","volume-title":"Interpolation of spatial data: some theory for kriging","author":"ML Stein","year":"1999","unstructured":"Stein ML (1999) Interpolation of spatial data: some theory for kriging. Springer, Berlin"},{"key":"1424_CR45","unstructured":"Titsias M (2009) Variational learning of inducing variables in sparse gaussian processes. In: Artificial intelligence and statistics, PMLR, pp 567\u2013574"},{"issue":"4","key":"1424_CR46","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1007\/s00158-008-0338-0","volume":"39","author":"FA Viana","year":"2009","unstructured":"Viana FA, Haftka RT, Steffen V (2009) Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct Multidiscip Optim 39(4):439\u2013457","journal-title":"Struct Multidiscip Optim"},{"issue":"8","key":"1424_CR47","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1109\/TNNLS.2012.2200299","volume":"23","author":"SE Yuksel","year":"2012","unstructured":"Yuksel SE, Wilson JN, Gader PD (2012) Twenty years of mixture of experts. IEEE Trans Neural Netw Learn Syst 23(8):1177\u20131193","journal-title":"IEEE Trans Neural Netw Learn Syst"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-023-01424-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-023-01424-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-023-01424-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T08:14:29Z","timestamp":1726215269000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-023-01424-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,27]]},"references-count":47,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["1424"],"URL":"https:\/\/doi.org\/10.1007\/s00180-023-01424-7","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,27]]},"assertion":[{"value":"8 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 October 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}