JuliaGaussianProcesses / JuliaGaussianProcesses/KernelFunctions.jl
Documenting caveats of `SimpleKernel`
Nobody has claimed this yet.
- Dominant language
- Julia
- Stars
- 275
- Forks
- 41
- PR merge metrics
- No merged PRs in 30d
Description
The docs recommend SimpleKernel for building ones own kernel using Distances.jl. They should probably here also note that not every PreMetric yields a positive-definite kernel.
In particular, as Theorem 1 of https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Feragen_Geodesic_Exponential_Kernels_2015_CVPR_paper.pdf notes, the geodesic distance for any "non-flat" manifold does not yield a positive-definite kernel when used in a squared exponential kernel, which would mean e.g. Distances.SphericalAngle will not yield a PD kernel.
Contributor 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.
Research direction
Start with the documented SimpleKernel section, especially the guidance for kernel functions depending on a metric. Check the linked Theorem 1 and the Distances.SphericalAngle example, then update the documentation to state that some PreMetric choices do not produce positive-definite kernels. Done means the caveat and example are clearly included in that section.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- julia
- Domain
- documentation, machine-learning
- Issue type
- Documentation
- Difficulty
- 2/5
- Estimated time
- 1-3 hours
- Activity status
- Stale
- Clarity
- Clearly specified
- Newbie friendliness
- 45/100