Implementing non-stationary gibbs kernel

Hi,

I'm new to Julia and Gaussian processes but recently came across a couple of interesting papers about non-stationary spectral mixture kernels [1], [2]. I can see that you have apready implemented a spectral mixture kernel here (As a side note I couldn't figure out how to get that to work)

I'm interested in trying to implement this but starting off small so just try to implement one part of this first which would be the input-dependent lengthscale kernel called the Gibbs kernel [3] which can be more easily see in [1] just before equation 7. (Just found another reference also here [4]).

I just took a screenshot from a talk that describes this so you can clearly see the difference between the typical RBF type kernel and this variable length-scale kernel.

Basically if you take the length-scale parameter from a Squared-Exponential Kernel and turn this into a function that depends on the input coordinates then you get a non-stationary kernel called the "Gibbs kernel".

The variable length-scale kernel has a learnable function \ell(x) which in [1] they parameterise by another GP.

Can anyone help me implementing this? From reading how KernelFunctions works this looks like it could be done easily using some kind of Transforms?

Thanks in advance for any help!

[1]: Non-Stationary Spectral Kernels
[2]: Neural Non-Stationary Spectral Kernel
[3]: Gibbs 1997
[4]: Nonstationary Covariance Functions for
Gaussian Process Regression (NIPS 2004)

Start by reviewing the existing spectral mixture kernel documentation and the KernelFunctions Transforms entry point mentioned in the issue, then compare the Gibbs kernel definitions in references [1], [3], and [4]. No implementation file or test is named; done would require an agreed API and a validated input-dependent lengthscale kernel.