Stochastic processes on manifolds

March 1, 2021 — March 1, 2021

Hilbert space
how do science
kernel tricks
machine learning
signal processing
stochastic processes
time series
Figure 1


1 References

Adler, Robert J. 2010. The Geometry of Random Fields.
Adler, Robert J., and Taylor. 2007. Random Fields and Geometry. Springer Monographs in Mathematics 115.
Adler, Robert J, Taylor, and Worsley. 2016. Applications of Random Fields and Geometry Draft.
Bhattacharya, and Bhattacharya. 2012. Nonparametric Inference on Manifolds: With Applications to Shape Spaces. Institute of Mathematical Statistics Monographs.
Borovitskiy, Terenin, Mostowsky, et al. 2020. Matérn Gaussian Processes on Riemannian Manifolds.” arXiv:2006.10160 [Cs, Stat].
Calandra, Peters, Rasmussen, et al. 2016. Manifold Gaussian Processes for Regression.” In 2016 International Joint Conference on Neural Networks (IJCNN).
Chikuse, and 筑瀬. 2003. Statistics on Special Manifolds.
Feragen, and Hauberg. 2016. Open Problem: Kernel Methods on Manifolds and Metric Spaces. What Is the Probability of a Positive Definite Geodesic Exponential Kernel? In Conference on Learning Theory.
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).
Manton. 2013. A Primer on Stochastic Differential Geometry for Signal Processing.” IEEE Journal of Selected Topics in Signal Processing.
Yaglom. 1961. Second-Order Homogeneous Random Fields.” Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Contributions to Probability Theory.