Miscellaneous nonstationary kernels

Kernels that are nonstationary constructed by other means than warping stationary ones.

Maybe start with Jun and Stein (2008);Fuglstad et al. (2015); Fuglstad et al. (2013)?


Bolin, David, and Kristin Kirchner. 2020. “The Rational SPDE Approach for Gaussian Random Fields With General Smoothness.” Journal of Computational and Graphical Statistics 29 (2): 274–85. https://doi.org/10.1080/10618600.2019.1665537.
Bolin, David, and Finn Lindgren. 2011. “Spatial Models Generated by Nested Stochastic Partial Differential Equations, with an Application to Global Ozone Mapping.” The Annals of Applied Statistics 5 (1): 523–50. https://doi.org/10.1214/10-AOAS383.
Fuglstad, Geir-Arne, Finn Lindgren, Daniel Simpson, and Håvard Rue. 2015. “Exploring a New Class of Non-Stationary Spatial Gaussian Random Fields with Varying Local Anisotropy.” Statistica Sinica 25 (1): 115–33. https://doi.org/10.5705/ss.2013.106w.
Fuglstad, Geir-Arne, Daniel Simpson, Finn Lindgren, and Håvard Rue. 2013. “Non-Stationary Spatial Modelling with Applications to Spatial Prediction of Precipitation,” 24.
Genton, Marc G. 2001. “Classes of Kernels for Machine Learning: A Statistics Perspective.” Journal of Machine Learning Research 2 (December): 299–312. http://jmlr.org/papers/volume2/genton01a/genton01a.pdf.
Genton, Marc G., and Olivier Perrin. 2004. “On a Time Deformation Reducing Nonstationary Stochastic Processes to Local Stationarity.” Journal of Applied Probability 41 (1, 1): 236–49. https://doi.org/10.1239/jap/1077134681.
Higdon, Dave. 2002. “Space and Space-Time Modeling Using Process Convolutions.” In Quantitative Methods for Current Environmental Issues, edited by Clive W. Anderson, Vic Barnett, Philip C. Chatwin, and Abdel H. El-Shaarawi, 37–56. London: Springer. https://doi.org/10.1007/978-1-4471-0657-9_2.
Higdon, David. 1998. “A Process-Convolution Approach to Modelling Temperatures in the North Atlantic Ocean.” Environmental and Ecological Statistics 5 (2): 173–90. https://doi.org/10.1023/A:1009666805688.
Hu, Xiangping, and Ingelin Steinsland. 2016. “Spatial Modeling with System of Stochastic Partial Differential Equations.” WIREs Computational Statistics 8 (2): 112–25. https://doi.org/10.1002/wics.1378.
Ingebrigtsen, Rikke, Finn Lindgren, and Ingelin Steinsland. 2014. “Spatial Models with Explanatory Variables in the Dependence Structure.” Spatial Statistics, Spatial Statistics Miami, 8 (May): 20–38. https://doi.org/10.1016/j.spasta.2013.06.002.
Jun, Mikyoung, and Michael L. Stein. 2008. “Nonstationary Covariance Models for Global Data.” The Annals of Applied Statistics 2 (4): 1271–89. https://doi.org/10.1214/08-AOAS183.
Kom Samo, Yves-Laurent, and Stephen Roberts. 2015. “Generalized Spectral Kernels.” June 7, 2015. http://arxiv.org/abs/1506.02236.
Lee, Herbert KH, Dave M Higdon, Catherine A Calder, and Christopher H Holloman. 2005. “Efficient Models for Correlated Data via Convolutions of Intrinsic Processes.” Statistical Modelling 5 (1): 53–74. https://doi.org/10.1191/1471082X05st085oa.
Lindgren, Finn, Håvard Rue, and Johan Lindström. 2011. “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (4): 423–98. https://doi.org/10.1111/j.1467-9868.2011.00777.x.
Paciorek, Christopher J., and Mark J. Schervish. 2003. “Nonstationary Covariance Functions for Gaussian Process Regression.” In Proceedings of the 16th International Conference on Neural Information Processing Systems, 16:273–80. NIPS’03. Cambridge, MA, USA: MIT Press. https://papers.nips.cc/paper/2003/hash/326a8c055c0d04f5b06544665d8bb3ea-Abstract.html.
———. 2006. “Spatial Modelling Using a New Class of Nonstationary Covariance Functions.” Environmetrics 17 (5): 483–506. https://doi.org/10.1002/env.785.
Remes, Sami, Markus Heinonen, and Samuel Kaski. 2017. “Non-Stationary Spectral Kernels.” In Advances in Neural Information Processing Systems 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, 4642–51. Curran Associates, Inc. http://papers.nips.cc/paper/7050-non-stationary-spectral-kernels.pdf.
Risser, Mark D., and Catherine A. Calder. 2015. “Regression-Based Covariance Functions for Nonstationary Spatial Modeling.” Environmetrics 26 (4): 284–97. https://doi.org/10.1002/env.2336.
Sampson, Paul D., and Peter Guttorp. 1992. “Nonparametric Estimation of Nonstationary Spatial Covariance Structure.” Journal of the American Statistical Association 87 (417): 108–19. https://doi.org/10.1080/01621459.1992.10475181.
Scharf, Henry R., Mevin B. Hooten, Devin S. Johnson, and John W. Durban. 2017. “Process Convolution Approaches for Modeling Interacting Trajectories.” November 21, 2017. http://arxiv.org/abs/1703.02112.
Ton, Jean-Francois, Seth Flaxman, Dino Sejdinovic, and Samir Bhatt. 2018. “Spatial Mapping with Gaussian Processes and Nonstationary Fourier Features.” Spatial Statistics 28 (December): 59–78. https://doi.org/10.1016/j.spasta.2018.02.002.
Wilkinson, William J., M. Riis Andersen, J. D. Reiss, D. Stowell, and A. Solin. 2019a. “Unifying Probabilistic Models for Time-Frequency Analysis.” In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 3352–56. https://doi.org/10.1109/ICASSP.2019.8682306.
Wilkinson, William J., Michael Riis Andersen, Joshua D. Reiss, Dan Stowell, and Arno Solin. 2019b. “End-to-End Probabilistic Inference for Nonstationary Audio Analysis.” January 31, 2019. https://arxiv.org/abs/1901.11436v1.

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