Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

WendlandKernel: Compact support -> sparse kernel matrix #550

Open
timweiland opened this issue Feb 12, 2024 · 0 comments
Open

WendlandKernel: Compact support -> sparse kernel matrix #550

timweiland opened this issue Feb 12, 2024 · 0 comments

Comments

@timweiland
Copy link

Hey 👋
I think Wendland kernels are cool, and I would like to contribute a PR. Let me know what you think :)

What's this about?

Wendland kernels have compact support. If two points are "too far away" (quantified by the lengthscale of the kernel), their covariance under a Wendland kernel is zero. This results in sparse kernel matrices, which can be leveraged to save memory and compute. In particular, Julia has built-in support for highly optimised sparse Cholesky decompositions.

Within their support, the Wendland functions are defined by a rational polynomial, the coefficients of which can be computed in closed form.

At the same time, Wendland kernels have nice theoretical properties. In particular, much like the Matérn kernels, their smoothness is controllable directly through a smoothness parameter.

For more details, and in particular for the definition of Wendland functions, refer to Chapter 9 of Scattered Data Approximation by Holger Wendland.

What do I propose?

I would like to add the WendlandKernel to KernelFunctions.jl. I already have an implementation locally for Wendland kernels with arbitrary space dimension $d$ and smoothness parameter $k$. It produces sparse kernel matrices.

Difficulties

Currently, AbstractGPs.jl does not work with sparse Cholesky factorizations. I added some extensions locally, and I am not sure if these should go to KernelFunctions.jl or if I should make a separate PR for AbstractGPs.jl.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

No branches or pull requests

1 participant