--- references: - id: AnderesConsistent2009 accessed: - year: 2021 month: 8 day: 12 author: - family: Anderes given: Ethan - family: Chatterjee given: Sourav citation-key: AnderesConsistent2009 container-title: The Annals of Statistics container-title-short: Ann. Statist. DOI: 10.1214/08-AOS647 ISSN: 0090-5364 issue: 5A issued: - year: 2009 month: 10 day: 1 title: >- Consistent estimates of deformed isotropic Gaussian random fields on the plane type: article-journal URL: http://arxiv.org/abs/0710.0379 volume: '37' - id: AnderesEstimating2008 accessed: - year: 2021 month: 8 day: 12 author: - family: Anderes given: Ethan B. - family: Stein given: Michael L. citation-key: AnderesEstimating2008 container-title: The Annals of Statistics DOI: 10.1214/009053607000000893 ISSN: 0090-5364, 2168-8966 issue: '2' issued: - year: 2008 month: 4 page: 719-741 publisher: Institute of Mathematical Statistics title: Estimating deformations of isotropic Gaussian random fields on the plane type: article-journal volume: '36' - id: BelkinUnderstand2018 accessed: - year: 2019 month: 6 day: 3 author: - family: Belkin given: Mikhail - family: Ma given: Siyuan - family: Mandal given: Soumik citation-key: BelkinUnderstand2018 container-title: International Conference on Machine Learning event-title: International Conference on Machine Learning issued: - year: 2018 month: 7 day: 3 language: en page: 541-549 title: To Understand Deep Learning We Need to Understand Kernel Learning type: paper-conference URL: http://arxiv.org/abs/1802.01396 - id: BohnRepresenter2018 accessed: - year: 2019 month: 11 day: 12 author: - family: Bohn given: Bastian - family: Griebel given: Michael - family: Rieger given: Christian citation-key: BohnRepresenter2018 container-title: arXiv:1709.10441 [cs, math] issued: - year: 2018 month: 6 day: 7 title: A representer theorem for deep kernel learning type: article-journal URL: http://arxiv.org/abs/1709.10441 - id: DamianBayesian2001 accessed: - year: 2021 month: 1 day: 14 author: - family: Damian given: Doris - family: Sampson given: Paul D. - family: Guttorp given: Peter citation-key: DamianBayesian2001 container-title: Environmetrics DOI: 10.1002/1099-095X(200103)12:2<161::AID-ENV452>3.0.CO;2-G ISSN: 1099-095X issue: '2' issued: - year: 2001 language: en page: 161-178 title: >- Bayesian estimation of semi-parametric non-stationary spatial covariance structures type: article-journal URL: https://sites.stat.washington.edu/NRCSE/pdf/trs39_bayes.pdf volume: '12' - id: FeragenOpen2016 accessed: - year: 2023 month: 3 day: 11 author: - family: Feragen given: Aasa - family: Hauberg given: Søren citation-key: FeragenOpen2016 container-title: Conference on Learning Theory event-title: Conference on Learning Theory ISSN: 1938-7228 issued: - year: 2016 month: 6 day: 6 language: en page: 1647-1650 publisher: PMLR title: >- Open Problem: Kernel methods on manifolds and metric spaces. What is the probability of a positive definite geodesic exponential kernel? type: paper-conference URL: https://proceedings.mlr.press/v49/feragen16.html - id: GentonClasses2001 accessed: - year: 2015 month: 12 day: 1 author: - family: Genton given: Marc G. citation-key: GentonClasses2001 container-title: Journal of Machine Learning Research ISSN: 1532-4435 issued: - year: 2001 month: 12 page: 299–312 title: 'Classes of Kernels for Machine Learning: A Statistics Perspective' type: article-journal URL: http://jmlr.org/papers/volume2/genton01a/genton01a.pdf volume: '2' - id: GentonTime2004 accessed: - year: 2021 month: 1 day: 5 author: - family: Genton given: Marc G. - family: Perrin given: Olivier citation-key: GentonTime2004 container-title: Journal of Applied Probability DOI: 10.1239/jap/1077134681 ISBN: '9781077134683' ISSN: 0021-9002, 1475-6072 issue: '1' issued: - year: 2004 month: 3 language: en number: '1' page: 236-249 publisher: Cambridge University Press title: >- On a time deformation reducing nonstationary stochastic processes to local stationarity type: article-journal volume: '41' - id: GibbsBayesian1998 accessed: - year: 2021 month: 3 day: 30 author: - family: Gibbs given: M. N. citation-key: GibbsBayesian1998 genre: Ph.D. issued: - year: 1998 language: eng publisher: University of Cambridge title: Bayesian Gaussian processes for regression and classification type: thesis URL: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599379 - id: HintonUsing2008 accessed: - year: 2019 month: 9 day: 19 author: - family: Hinton given: Geoffrey E - family: Salakhutdinov given: Ruslan R citation-key: HintonUsing2008 container-title: Advances in Neural Information Processing Systems 20 editor: - family: Platt given: J. C. - family: Koller given: D. - family: Singer given: Y. - family: Roweis given: S. T. issued: - year: 2008 page: 1249–1256 publisher: Curran Associates, Inc. title: Using Deep Belief Nets to Learn Covariance Kernels for Gaussian Processes type: paper-conference URL: >- http://papers.nips.cc/paper/3211-using-deep-belief-nets-to-learn-covariance-kernels-for-gaussian-processes.pdf - id: IkedaComposition2021 accessed: - year: 2021 month: 3 day: 30 author: - family: Ikeda given: Masahiro - family: Ishikawa given: Isao - family: Sawano given: Yoshihiro citation-key: IkedaComposition2021 container-title: arXiv:1911.11992 [math, stat] issued: - year: 2021 month: 3 day: 9 title: >- Composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions type: article-journal URL: http://arxiv.org/abs/1911.11992 - id: PaciorekNonstationary2003 accessed: - year: 2021 month: 3 day: 29 author: - family: Paciorek given: Christopher J. - family: Schervish given: Mark J. citation-key: PaciorekNonstationary2003 collection-title: NIPS'03 container-title: >- Proceedings of the 16th International Conference on Neural Information Processing Systems event-place: Cambridge, MA, USA issued: - year: 2003 month: 12 day: 9 page: 273–280 publisher: MIT Press publisher-place: Cambridge, MA, USA title: Nonstationary covariance functions for Gaussian process regression type: paper-conference URL: >- https://papers.nips.cc/paper/2003/hash/326a8c055c0d04f5b06544665d8bb3ea-Abstract.html volume: '16' - id: PerrinReducing1999 accessed: - year: 2021 month: 1 day: 5 author: - family: Perrin given: Olivier - family: Senoussi given: Rachid citation-key: PerrinReducing1999 container-title: Statistics & Probability Letters container-title-short: Statistics & Probability Letters DOI: 10.1016/S0167-7152(98)00278-8 ISSN: 0167-7152 issue: '4' issued: - year: 1999 month: 7 day: 15 language: en page: 393-397 title: >- Reducing non-stationary stochastic processes to stationarity by a time deformation type: article-journal volume: '43' - id: PerrinReducing2000 accessed: - year: 2021 month: 1 day: 5 author: - family: Perrin given: Olivier - family: Senoussi given: Rachid citation-key: PerrinReducing2000 container-title: Statistics & Probability Letters container-title-short: Statistics & Probability Letters DOI: 10.1016/S0167-7152(99)00188-1 ISSN: 0167-7152 issue: '1' issued: - year: 2000 month: 5 day: 15 language: en page: 23-32 title: >- Reducing non-stationary random fields to stationarity and isotropy using a space deformation type: article-journal volume: '48' - id: RasmussenGaussian2006 author: - family: Rasmussen given: Carl Edward - family: Williams given: Christopher K. I. call-number: QA274.4 .R37 2006 citation-key: RasmussenGaussian2006 collection-title: Adaptive computation and machine learning event-place: Cambridge, Mass ISBN: 978-0-262-18253-9 issued: - year: 2006 number-of-pages: '248' page: '248' publisher: MIT Press publisher-place: Cambridge, Mass title: Gaussian processes for machine learning type: book URL: http://www.gaussianprocess.org/gpml/ - id: SampsonNonparametric1992 accessed: - year: 2021 month: 1 day: 5 author: - family: Sampson given: Paul D. - family: Guttorp given: Peter citation-key: SampsonNonparametric1992 container-title: Journal of the American Statistical Association DOI: 10.1080/01621459.1992.10475181 ISSN: 0162-1459 issue: '417' issued: - year: 1992 month: 3 day: 1 page: 108-119 publisher: Taylor & Francis title: Nonparametric Estimation of Nonstationary Spatial Covariance Structure type: article-journal volume: '87' - id: SchmidtBayesian2003 accessed: - year: 2021 month: 1 day: 14 author: - family: Schmidt given: Alexandra M. - family: O’Hagan given: Anthony citation-key: SchmidtBayesian2003 container-title: 'Journal of the Royal Statistical Society: Series B (Statistical Methodology)' DOI: 10.1111/1467-9868.00413 ISSN: 1467-9868 issue: '3' issued: - year: 2003 language: en page: 743-758 publisher: Royal Statistical Society title: >- Bayesian inference for non-stationary spatial covariance structure via spatial deformations type: article-journal URL: https://ideas.repec.org/a/bla/jorssb/v65y2003i3p743-758.html volume: '65' - id: ShimotsuLocal2004 accessed: - year: 2020 month: 5 day: 28 author: - family: Shimotsu given: Katsumi - family: Phillips given: Peter C. B. citation-key: ShimotsuLocal2004 container-title: The Annals of Statistics container-title-short: Ann. Statist. DOI: 10.1214/009053604000000139 ISSN: 0090-5364 issue: '2' issued: - year: 2004 month: 4 language: en page: 656-692 title: Local Whittle estimation in nonstationary and unit root cases type: article-journal volume: '32' - id: SnoekInput2014 author: - family: Snoek given: Jasper - family: Swersky given: Kevin - family: Zemel given: Rich - family: Adams given: Ryan citation-key: SnoekInput2014 container-title: >- Proceedings of the 31st International Conference on Machine Learning (ICML-14) event-title: International Conference on Machine Learning issued: - year: 2014 page: 1674–1682 title: Input Warping for Bayesian Optimization of Non-Stationary Functions type: paper-conference URL: http://www.jmlr.org/proceedings/papers/v32/snoek14.pdf - id: TompkinsFourier2018 accessed: - year: 2021 month: 1 day: 25 author: - family: Tompkins given: Anthony - family: Ramos given: Fabio citation-key: TompkinsFourier2018 container-title: Proceedings of the AAAI Conference on Artificial Intelligence container-title-short: AAAI ISSN: 2374-3468 issue: '1' issued: - year: 2018 month: 4 day: 29 language: en number: '1' title: Fourier Feature Approximations for Periodic Kernels in Time-Series Modelling type: article-journal URL: https://ojs.aaai.org/index.php/AAAI/article/view/11696 volume: '32' - id: VuModeling2020 accessed: - year: 2021 month: 7 day: 6 author: - family: Vu given: Quan - family: Zammit-Mangion given: Andrew - family: Cressie given: Noel citation-key: VuModeling2020 DOI: 10.5705/ss.202020.0156 issued: - year: 2020 month: 4 day: 18 language: en title: >- Modeling Nonstationary and Asymmetric Multivariate Spatial Covariances via Deformations type: article-journal URL: https://arxiv.org/abs/2004.08724v2 - id: WilsonDeep2016 accessed: - year: 2020 month: 10 day: 31 author: - family: Wilson given: Andrew Gordon - family: Hu given: Zhiting - family: Salakhutdinov given: Ruslan - family: Xing given: Eric P. citation-key: WilsonDeep2016 container-title: Artificial Intelligence and Statistics event-title: Artificial Intelligence and Statistics ISSN: 1938-7228 issued: - year: 2016 month: 5 day: 2 language: en page: 370-378 publisher: PMLR title: Deep Kernel Learning type: paper-conference URL: http://proceedings.mlr.press/v51/wilson16.html - id: ZammitMangionDeep2021 accessed: - year: 2021 month: 7 day: 6 author: - family: Zammit-Mangion given: Andrew - family: Ng given: Tin Lok James - family: Vu given: Quan - family: Filippone given: Maurizio citation-key: ZammitMangionDeep2021 container-title: Journal of the American Statistical Association DOI: 10.1080/01621459.2021.1887741 ISSN: 0162-1459 issue: '0' issued: - year: 2021 month: 2 day: 12 page: 1-22 publisher: Taylor & Francis title: Deep Compositional Spatial Models type: article-journal volume: '0' ...