Miscellaneous nonstationary kernels

September 16, 2019 — January 21, 2021

Hilbert space
kernel tricks
signal processing
stochastic processes
Figure 1

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)?

1 References

Bolin, and Kirchner. 2020. The Rational SPDE Approach for Gaussian Random Fields With General Smoothness.” Journal of Computational and Graphical Statistics.
Bolin, and Lindgren. 2011. Spatial Models Generated by Nested Stochastic Partial Differential Equations, with an Application to Global Ozone Mapping.” The Annals of Applied Statistics.
Fuglstad, Lindgren, Simpson, et al. 2015. Exploring a New Class of Non-Stationary Spatial Gaussian Random Fields with Varying Local Anisotropy.” Statistica Sinica.
Fuglstad, Simpson, Lindgren, et al. 2013. “Non-Stationary Spatial Modelling with Applications to Spatial Prediction of Precipitation.”
Genton. 2001. Classes of Kernels for Machine Learning: A Statistics Perspective.” Journal of Machine Learning Research.
Genton, and Perrin. 2004. On a Time Deformation Reducing Nonstationary Stochastic Processes to Local Stationarity.” Journal of Applied Probability.
Higdon, David. 1998. A Process-Convolution Approach to Modelling Temperatures in the North Atlantic Ocean.” Environmental and Ecological Statistics.
Higdon, Dave. 2002. Space and Space-Time Modeling Using Process Convolutions.” In Quantitative Methods for Current Environmental Issues.
Hu, and Steinsland. 2016. Spatial Modeling with System of Stochastic Partial Differential Equations.” WIREs Computational Statistics.
Ingebrigtsen, Lindgren, and Steinsland. 2014. Spatial Models with Explanatory Variables in the Dependence Structure.” Spatial Statistics, Spatial Statistics Miami,.
Jun, and Stein. 2008. Nonstationary Covariance Models for Global Data.” The Annals of Applied Statistics.
Kom Samo, and Roberts. 2015. Generalized Spectral Kernels.” arXiv:1506.02236 [Stat].
Lee, Higdon, Calder, et al. 2005. Efficient Models for Correlated Data via Convolutions of Intrinsic Processes.” Statistical Modelling.
Lindgren, Rue, and 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).
Noack, Luo, and Risser. 2023. A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes.”
Paciorek, and Schervish. 2003. Nonstationary Covariance Functions for Gaussian Process Regression.” In Proceedings of the 16th International Conference on Neural Information Processing Systems. NIPS’03.
———. 2006. Spatial Modelling Using a New Class of Nonstationary Covariance Functions.” Environmetrics.
Remes, Heinonen, and Kaski. 2017. Non-Stationary Spectral Kernels.” In Advances in Neural Information Processing Systems 30.
Risser, and Calder. 2015. Regression-Based Covariance Functions for Nonstationary Spatial Modeling.” Environmetrics.
Sampson, and Guttorp. 1992. Nonparametric Estimation of Nonstationary Spatial Covariance Structure.” Journal of the American Statistical Association.
Scharf, Hooten, Johnson, et al. 2017. Process Convolution Approaches for Modeling Interacting Trajectories.” arXiv:1703.02112 [Stat].
Ton, Flaxman, Sejdinovic, et al. 2018. Spatial Mapping with Gaussian Processes and Nonstationary Fourier Features.” Spatial Statistics.
Wilkinson, Andersen, Reiss, et al. 2019a. End-to-End Probabilistic Inference for Nonstationary Audio Analysis.” arXiv:1901.11436 [Cs, Eess, Stat].
Wilkinson, Andersen, Reiss, et al. 2019b. Unifying Probabilistic Models for Time-Frequency Analysis.” In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).