{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:46:48Z","timestamp":1761965208908,"version":"3.37.3"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,7,9]],"date-time":"2020-07-09T00:00:00Z","timestamp":1594252800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,9]],"date-time":"2020-07-09T00:00:00Z","timestamp":1594252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s00180-020-01011-0","type":"journal-article","created":{"date-parts":[[2020,7,9]],"date-time":"2020-07-09T19:07:46Z","timestamp":1594321666000},"page":"347-373","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Robust weighted Gaussian processes"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2263-4931","authenticated-orcid":false,"given":"Ruben","family":"Ramirez-Padron","sequence":"first","affiliation":[]},{"given":"Boris","family":"Mederos","sequence":"additional","affiliation":[]},{"given":"Avelino J.","family":"Gonzalez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,9]]},"reference":[{"key":"1011_CR1","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/s00180-011-0301-1","volume":"28","author":"C Agostinelli","year":"2013","unstructured":"Agostinelli C, Greco L (2013) A weighted strategy to handle likelihood uncertainty in Bayesian inference. Comput Stat 28:319\u2013339","journal-title":"Comput Stat"},{"issue":"1","key":"1011_CR2","doi-asserted-by":"publisher","first-page":"726","DOI":"10.1093\/mnras\/stw1618","volume":"462","author":"IA Almosallam","year":"2016","unstructured":"Almosallam IA, Jarvis MJ, Roberts SJ (2016) GPz: non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts. Mon Not R Astron Soc 462(1):726\u2013739","journal-title":"Mon Not R Astron Soc"},{"issue":"4","key":"1011_CR3","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1145\/358841.358850","volume":"23","author":"JL Bentley","year":"1980","unstructured":"Bentley JL (1980) Multidimensional divide and conquer. Commun ACM 23(4):214\u2013229","journal-title":"Commun ACM"},{"key":"1011_CR4","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1016\/j.tcs.2004.08.005","volume":"326","author":"T Bernholt","year":"2004","unstructured":"Bernholt T, Fischer P (2004) The complexity of computing the MCD-estimator. Theor Comput Sci 326:383\u2013398","journal-title":"Theor Comput Sci"},{"key":"1011_CR5","volume-title":"Pattern recognition and machine learning","author":"CM Bishop","year":"2006","unstructured":"Bishop CM (2006) Pattern recognition and machine learning. Springer, New York"},{"key":"1011_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1086\/191190","volume":"64","author":"R Buta","year":"1987","unstructured":"Buta R (1987) The structure and dynamics of ringed galaxies, III: surface photometry and kinematics of the ringed nonbarred spiral NGC7531. Astrophys J Suppl Ser 64:1\u201337","journal-title":"Astrophys J Suppl Ser"},{"key":"1011_CR7","unstructured":"Csat\u00f3 L (2002) Gaussian processes\u2014iterative sparse approximations. PhD thesis. Aston University, Birmingham, UK. http:\/\/publications.aston.ac.uk\/id\/eprint\/1327\/"},{"issue":"3","key":"1011_CR8","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1162\/089976602317250933","volume":"14","author":"L Csat\u00f3","year":"2002","unstructured":"Csat\u00f3 L, Opper M (2002) Sparse on-line Gaussian processes. Neural Comput 14(3):641\u2013668","journal-title":"Neural Comput"},{"key":"1011_CR9","volume-title":"Practical guide to splines. Applied mathematical sciences","author":"CA de Boor","year":"2001","unstructured":"de Boor CA (2001) Practical guide to splines. Applied mathematical sciences, vol 27, revised edn. Springer, New York","edition":"revised"},{"issue":"4","key":"1011_CR10","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1080\/03610917808812083","volume":"7","author":"JE Dennis Jr","year":"1978","unstructured":"Dennis JE Jr, Welsch RE (1978) Techniques for nonlinear least squares and robust regression. Commun Stat Simul Comput 7(4):345\u2013359","journal-title":"Commun Stat Simul Comput"},{"key":"1011_CR11","unstructured":"Drucker H, Burges CJ, Kaufman L, Smola AJ, Vapnik V (1997) Support vector regression machines. Advances in neural information processing systems, pp 155\u2013161"},{"issue":"S1","key":"1011_CR12","doi-asserted-by":"publisher","first-page":"S19","DOI":"10.1002\/jae.3950080504","volume":"8","author":"J Geweke","year":"1993","unstructured":"Geweke J (1993) Bayesian treatment of the independent Student-t linear model. J Appl Econom 8(S1):S19\u2013S40","journal-title":"J Appl Econom"},{"key":"1011_CR13","unstructured":"Girden ER (1992) ANOVA: repeated measures. Sage University Paper Series on Quantitative Applications in the Social Sciences 07-084, Sage University, Newbury Park, CA"},{"issue":"5","key":"1011_CR14","doi-asserted-by":"publisher","first-page":"1258","DOI":"10.1016\/j.jspi.2007.05.001","volume":"138","author":"L Greco","year":"2008","unstructured":"Greco L, Racugno W, Ventura L (2008) Robust likelihood functions in Bayesian analysis. J Stat Plan Inference 138(5):1258\u20131270","journal-title":"J Stat Plan Inference"},{"key":"1011_CR15","volume-title":"Robust statistics. The approach based on influence functions","author":"FR Hampel","year":"1986","unstructured":"Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics. The approach based on influence functions. Wiley, New York"},{"issue":"1","key":"1011_CR16","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1214\/aoms\/1177703732","volume":"53","author":"PJ Huber","year":"1964","unstructured":"Huber PJ (1964) Robust estimation of a location parameter. Ann Stat 53(1):73\u2013101","journal-title":"Ann Stat"},{"key":"1011_CR17","doi-asserted-by":"publisher","DOI":"10.1002\/0471725250","volume-title":"Robust statistics","author":"PJ Huber","year":"1981","unstructured":"Huber PJ, Ronchetti EM (1981) Robust statistics. Wiley, New York"},{"key":"1011_CR18","first-page":"3227","volume":"12","author":"P Jyl\u00e4nki","year":"2011","unstructured":"Jyl\u00e4nki P, Vanhatalo J, Vehtari A (2011) Robust Gaussian process regression with a student-t likelihood. J Mach Learn Res 12:3227\u20133257","journal-title":"J Mach Learn Res"},{"key":"1011_CR19","doi-asserted-by":"crossref","unstructured":"Kemmler M, Rodner E, Denzler J (2010) One-class classification with Gaussian processes. In: Proceedings of the Asian conference on computer vision. Lecture notes in computer science, vol 6493. Springer, pp 489\u2013500","DOI":"10.1007\/978-3-642-19309-5_38"},{"key":"1011_CR20","unstructured":"Kuss M (2006) Gaussian process models for robust regression, classification, and reinforcement learning. Doctoral dissertation, Technische Universit\u00e4t Darmstadt, Germany. http:\/\/hdl.handle.net\/11858\/00-001M-0000-0013-D2CD-C"},{"key":"1011_CR21","unstructured":"Kuss M, Pfingsten T, Csat\u00f3L, Rasmussen CE (2005) Approximate inference for robust Gaussian process regression. Max Planck Institute for Biological Cybernetics, T\u00fcbingen, Germany, Technical Report 136. http:\/\/hdl.handle.net\/11858\/00-001M-0000-0013-D703-4"},{"key":"1011_CR22","doi-asserted-by":"crossref","unstructured":"Le QV, Smola AJ, Canu S (2005) Heteroscedastic Gaussian process regression. In: Proceedings of the 22nd international conference on machine learning. ACM, pp 489\u2013496","DOI":"10.1145\/1102351.1102413"},{"key":"1011_CR23","first-page":"133","volume-title":"Neural networks and machine learning. NATO ASI series","author":"DJC MacKay","year":"1998","unstructured":"MacKay DJC (1998) Introduction to Gaussian processes. In: Bishop CM (ed) Neural networks and machine learning. NATO ASI series, vol 168. Springer, Berlin, pp 133\u2013165"},{"issue":"1","key":"1011_CR24","first-page":"49","volume":"2","author":"PC Mahalanobis","year":"1936","unstructured":"Mahalanobis PC (1936) On the generalised distance in statistics. Proc Natl Inst Sci India 2(1):49\u201355","journal-title":"Proc Natl Inst Sci India"},{"key":"1011_CR25","doi-asserted-by":"publisher","DOI":"10.1002\/0470010940","volume-title":"Robust statistics: theory and methods","author":"RA Maronna","year":"2006","unstructured":"Maronna RA, Martin DR, Yohai VJ (2006) Robust statistics: theory and methods. Wiley, Chichester"},{"key":"1011_CR26","doi-asserted-by":"crossref","unstructured":"Mattos CLC, Santos JDA, Barreto GA (2015) An empirical evaluation of robust Gaussian process models for system identification. In: International conference on intelligent data engineering and automated learning. Springer, Cham, pp 172\u2013180","DOI":"10.1007\/978-3-319-24834-9_21"},{"key":"1011_CR27","unstructured":"Minka TP (2001) Expectation propagation for approximate Bayesian Inference. In: Proceedings of the seventeenth conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers Inc., pp 362\u2013369"},{"key":"1011_CR28","doi-asserted-by":"crossref","unstructured":"Murphy L, Martin S, Corke P (2012) Creating and using probabilistic cost maps from vehicle experience. In: Proceedings of IEEE\/RSJ international conference on intelligent robots and systems, intelligent robots and systems (IROS). IEEE, pp 4689\u20134694","DOI":"10.1109\/IROS.2012.6386118"},{"key":"1011_CR29","unstructured":"Neal RM (1997) Monte Carlo implementation of Gaussian process models for Bayesian regression and classification. Technical Report 9702, Department of Statistics and Department of Computer Science, University of Toronto. arXiv:physics\/9701026"},{"key":"1011_CR30","volume-title":"On-line learning in neural networks","author":"M Opper","year":"1998","unstructured":"Opper M (1998) A Bayesian approach to on-line learning. In: Saad D (ed) On-line learning in neural networks. Cambridge University Press, Cambridge"},{"key":"1011_CR31","unstructured":"Ramirez-Padron R (2015) Batch and online implicit weighted Gaussian processes for robust Novelty detection. Doctoral dissertation, University of Central Florida. http:\/\/purl.fcla.edu\/fcla\/etd\/CFE0005869"},{"key":"1011_CR32","unstructured":"Ramirez-Padron R, Mederos B, Gonzalez AJ (2013) Novelty detection using sparse online Gaussian processes for visual object recognition. In: International FLAIRS conference. St. Pete Beach, FL, USA, pp 124\u2013129"},{"key":"1011_CR33","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.jprocont.2016.04.003","volume":"42","author":"R Ranjan","year":"2016","unstructured":"Ranjan R, Huang B, Fatehi A (2016) Robust Gaussian process modeling using EM algorithm. J Process Control 42:125\u2013136","journal-title":"J Process Control"},{"key":"1011_CR34","volume-title":"Gaussian processes for machine learning","author":"CE Rasmussen","year":"2006","unstructured":"Rasmussen CE, Williams C (2006) Gaussian processes for machine learning. MIT Press, Cambridge"},{"key":"1011_CR35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69389-2","volume-title":"Introduction to robust and quasi-robust statistical methods","author":"WJJ Rey","year":"1983","unstructured":"Rey WJJ (1983) Introduction to robust and quasi-robust statistical methods. Springer, Berlin"},{"key":"1011_CR36","doi-asserted-by":"crossref","unstructured":"Rottmann A, Burgard W (2010) Learning non-stationary system dynamics online using Gaussian processes. In: Proceedings of 32nd DAGM symposium, Darmstadt, Germany, pp 192\u2013201","DOI":"10.1007\/978-3-642-15986-2_20"},{"issue":"388","key":"1011_CR37","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1080\/01621459.1984.10477105","volume":"79","author":"PJ Rousseeuw","year":"1984","unstructured":"Rousseeuw PJ (1984) Least median of squares regression. J Am Stat Assoc 79(388):871\u2013880","journal-title":"J Am Stat Assoc"},{"key":"1011_CR38","unstructured":"Schmidt G, Mattern R, Sch\u00fcler F (1981) Biomechanical investigation to determine physical and traumatological differentiation criteria for the maximum load capacity of head and vertebral column with and without protective helmet under effects of impact. EEC Research Program on Biomechanics of Impacts, Final Report Phase III, Project 65, Institut f\u00fcr Rechtsmedizin, Universit\u00e4t Heidelberg, Germany"},{"issue":"2","key":"1011_CR39","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1142\/S0129065704001899","volume":"14","author":"M Seeger","year":"2004","unstructured":"Seeger M (2004) Gaussian processes for machine learning. Int J Neural Syst 14(2):69\u2013106","journal-title":"Int J Neural Syst"},{"key":"1011_CR40","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809682","volume-title":"Kernel methods for pattern analysis","author":"J Shawe-Taylor","year":"2004","unstructured":"Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, Cambridge"},{"issue":"1","key":"1011_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1985.tb01327.x","volume":"47","author":"BW Silverman","year":"1985","unstructured":"Silverman BW (1985) Some aspects of the spline smoothing approach to non-parametric curve fitting. J R Stat Soc Ser B (Methodol) 47(1):1\u201352","journal-title":"J R Stat Soc Ser B (Methodol)"},{"key":"1011_CR42","first-page":"985","volume":"8","author":"M Sugiyama","year":"2007","unstructured":"Sugiyama M, Krauledat M, M\u00fcller KR (2007) Covariate shift adaptation by importance weighted cross validation. J Mach Learn Res 8:985\u20131005","journal-title":"J Mach Learn Res"},{"key":"1011_CR43","unstructured":"Tipping ME (2000) The relevance vector machine. In: Advances in neural information processing systems, pp 652\u2013658"},{"issue":"1\u20133","key":"1011_CR44","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.neucom.2005.02.016","volume":"69","author":"ME Tipping","year":"2005","unstructured":"Tipping ME, Lawrence ND (2005) Variational inference for Student-t models: robust Bayesian interpolation and generalised component analysis. Neurocomputing 69(1\u20133):123\u2013141","journal-title":"Neurocomputing"},{"key":"1011_CR45","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/j.chemolab.2004.06.003","volume":"75","author":"S Verboven","year":"2005","unstructured":"Verboven S, Hubert M (2005) LIBRA: a MATLAB Library for robust analysis. Chemometr Intell Lab Syst 75:127\u2013136","journal-title":"Chemometr Intell Lab Syst"},{"key":"1011_CR46","doi-asserted-by":"crossref","unstructured":"Wald I, Havran V (2006) On building fast kd-trees for ray tracing, and on doing that in O(N log N). In: Proceedings of the 2006 IEEE symposium on interactive ray tracing, pp 61\u201369","DOI":"10.1109\/RT.2006.280216"},{"key":"1011_CR47","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1016\/j.asoc.2018.12.029","volume":"76","author":"B Wang","year":"2019","unstructured":"Wang B, Mao Z (2019) Outlier detection based on Gaussian process with application to industrial processes. Appl Soft Comput J 76:505\u2013516","journal-title":"Appl Soft Comput J"},{"issue":"3","key":"1011_CR48","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1111\/j.2517-6161.1984.tb01317.x","volume":"46","author":"M West","year":"1984","unstructured":"West M (1984) Outlier models and prior distributions in Bayesian linear regression. J R Stat Soc (Ser B) 46(3):431\u2013439","journal-title":"J R Stat Soc (Ser B)"},{"issue":"20","key":"1011_CR49","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.1109\/34.735807","volume":"12","author":"CKI Williams","year":"1998","unstructured":"Williams CKI, Barber D (1998) Bayesian classification with Gaussian processes. IEEE Trans Pattern Anal Mach Intell 12(20):1342\u20131351","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"12","key":"1011_CR50","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1016\/S0008-8846(98)00165-3","volume":"28","author":"C Yeh","year":"1998","unstructured":"Yeh C (1998) Modeling of strength of high performance concrete using artificial neural networks. Cem Concr Res 28(12):1797\u20131808","journal-title":"Cem Concr Res"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-020-01011-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-020-01011-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-020-01011-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T18:21:47Z","timestamp":1723227707000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-020-01011-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,9]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["1011"],"URL":"https:\/\/doi.org\/10.1007\/s00180-020-01011-0","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"type":"print","value":"0943-4062"},{"type":"electronic","value":"1613-9658"}],"subject":[],"published":{"date-parts":[[2020,7,9]]},"assertion":[{"value":"10 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 June 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 July 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}