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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.
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?
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[-]Is it possible to use Gibbs for 2d?[/-][+]Is it possible to extend Gibbs for 2d?[/+]bwengals commentedon Jul 12, 2023
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 xw(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 commentedon Jul 17, 2023
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 commentedon Jul 24, 2023
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 commentedon Jul 25, 2023
What do you suggest for non monotonous?
ferrine commentedon Jul 25, 2023
Ah, seems like I get that,