In this section, we will look at some of the staple methods for nonparametric interpolation. We will outline each
- Naive Whirlwind Tour with applications for Data Assimilation
- Nearest Neighbours
- K-NN
- Weighted Distances
- Scaling the Algorithm - KDTree + BallTree
- Scaling the hardware - parallelization, GPU hardware
- Kernel Density Estimation
- KDE
- FFT for Equidistant Grids
- scaling the hardware - GPU hardware
- Regression
- Gaussian Processes
- Appendix: Playing with All things Gaussian
- Spatial Autocorrelation with (Semi-)Variograms
- 3 Views of GPs
- GP with Numpyro
- Scaling - Kernel Approximations
- Scaling - Inducing Points
- Scaling -
- Appendix GPs in practice
- From Scratch
- With TinyGP & GPJax
- With PPL Numpyro
- Customizing the Numpyro Implementation
- Distances
- Kernel Matrices
- Kernel Matrix Derivatives
- Improved Gaussian Processes
- Moment-Based
- Sparse GPs
- SVGPs
- Structured GPs
- Deep Kernel Learning
- Basis Functions
- Fourier Features GP
- Spherical Harmonics GP
- Sparse Spherical Harmonics GPs
- Moment-Based