I want to use Gaussion Process Regression to fit a function to data. Since I know a little about the target function, I would like to build a suitable kernel from existing kernels. The input vector consists of two parameters, so my kernel or covariance function is two-dimensional.
I combined a 2D radial basis function kernel with the same variance and lengthscale on both dimensions by adding an linear kernel.
K1 = RBF(2D) + Linear (1D)
For a small local variance I added another 1D radial basis function kernel with a greater variance and lengthscale then the already used RBF-Kernel.
My result looks like: Surfaceplot (A survace with a valley parallel to an axes / in one dimension.)
What I'm really looking for is a kernel or covariance function, that is not parallel to an axes, but has an valey across both dimensions like: Kernel Cookbook
Has anyone a sugestion?
(Im using Python 3.10.0 with GPy.)