JuliaGaussianProcesses / JuliaGaussianProcesses/KernelFunctions.jl

Spectral distribution and domain of kernel input

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Dominant language
Julia
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Forks
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Description

I'd like to have a function spectral_distribution which takes a kernel defined over R^d and returns in spectral distribution. For example

function spectral_distribution(k::SqExponentialKernel)
  MvNormal(dim(k), ones(dim(k)))
end

However, there is one big API incompatibility with such a method: currently, there is no way to determine what domain a KernelFunctions.jl kernel is defined over. In particular, there's no way to tell whether a given kernel is defined over R^1 or R^3 or R^100. The underlying issue is that Distances.jl does not distinguish this, and KernelFunctions.jl largely works on top of that API. This is also an issue for #9 and #10.

I suggest instead adding the domain as an explicit parameter to the kernel.

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Research direction

Start by reviewing the KernelFunctions.jl kernel API and the Distances.jl assumptions that prevent a kernel's domain dimension from being identified. Compare the proposed spectral_distribution function and explicit domain parameter with the concerns in issues #9 and #10. Done means the API direction is resolved for determining kernel domains and supporting spectral distributions.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
backend-api-design, machine-learning
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
28/100

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