`WendlandKernel`: Compact support -> sparse kernel matrix
Nobody has claimed this yet.
Assessment
- Difficulty
- 5/5
- Estimated time
- Over a week
- Newbie friendliness
- 25/100
- Issue type
- Feature
- Clarity
- Mostly clear
- Activity status
- Stale
- Tech stack
- julia
- Domain
- machine-learning
Research direction
Start by reviewing the proposed WendlandKernel implementation in KernelFunctions.jl and the existing kernel abstractions, then investigate how sparse kernel matrices are represented. Check the interaction with AbstractGPs.jl and determine whether sparse Cholesky support belongs in that project or a separate change; done requires agreement on this scope and a working kernel implementation.
Written by the indexing model from the issue text.
Description
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.
- Dominant language
- Julia
- Stars
- 276
- Forks
- 42
- Avg merge
- 19h
- Merged PRs (30d)
- 2
Getting set up
- No Dockerfile or Docker Compose file
- Has a pull request template
- Read the contributing guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
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