Is it possible to extend Gibbs for 2d?

[ferrine]

In the original implementation, there is reference that Gibbs kernel is only supported for 1d inputs.

pymc/pymc/gp/cov.py

Line 817 in f67ff8b

class Gibbs(Covariance):

An interesting application is 2d, where there are spatial coordinates and varying length scale due to geological differences or regional factors.

@bwengals what do you think?

[bwengals]

That would be interesting, and yes a Gibbs kernel works in 2d. The code in the repo you linked just says its "untested" in 2d but I bet it could be made to work pretty easily, if it doesn't already. Another option to get nonstationary behavior is by warping the inputs, so instead of passing x pass some function of x w(x, theta). All the GP codes should work with pytensor inputs, so this is compatible with approximations like HSGP. The warping function does have to be monotonic though.

[ferrine]

The warping function does have to be monotonic though.

That's an important take. So in case I have non homogenous lengthscale that can get smaller, than bigger, that would not work. Maybe instead there should be some Riemannian theory involved to put this GP onto the tangent space, right?

[bwengals]

lengthscale that can get smaller, than bigger

You can still do that via warping, v]https://www.pymc.io/projects/examples/en/latest/gaussian_processes/GP-MeansAndCovs.html#applying-an-arbitrary-warping-function-on-the-inputs

Monotonic, but large slope = small lengthscale, small slope = long lengthscale

[ferrine]

What do you suggest for non monotonous?

[ferrine]

Ah, seems like I get that,