Add HSGP contribution module

[juanitorduz]

Closes #1788

Motivation: As described in the issue

I have been using the Hilber Space approximation for Gaussian Processes a lot. The main ingredients are the spectral densities of the kernels and the eigenvalues and eigenvectors of the Laplacian in a box, see https://num.pyro.ai/en/stable/examples/hsgp.html

Scope of this PR:

• Basic module and descriiption
• Docstrings
• Tests
• Documentation
• Example Notebook

I would consider this module experimental to get user feedback (as described in the docs). For now, it just supports one-dimensional inputs (my most common use case). In the next iteration, I will add an extension to higher dimensions. I did not want to over-complicate this first PR.

Happy to get feedback :)

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[martinjankowiak]

it'd be great to get feedback from @omarfsosa who wrote the hsgp example in the first place

[juanitorduz]

I did not know @omarfsosa was the original author. I give credit to the example in many places, but I can also add his name (or GitHub handle) to the docs as I'm essentially organizing the functions from the example and adding docs and tests 😄

[juanitorduz]

I did not know @omarfsosa was the original author. I give credit to the example in many places, but I can also add his name (or GitHub handle) to the docs as I'm essentially organizing the functions from the example and adding docs and tests 😄

Added reference to original author to the module page in 2b1e37d

[omarfsosa]

This is really cool @juanitorduz ! I've often reused some of those functions but found myself copy-pasting stuff cause I never had the time to write it properly so I really appreciate this. I think it's looking really good, my only nit would be the naming of the "ell" parameter in some of the functions, but I can see why you did that and tbh I don't have a better suggestion for now.

[juanitorduz]

Thanks for the feedback! Exactly! I was copy pasting this a lot as well 😄!

Regarding the variable name: the original name is L but I don't find it esthetic as it is upper case and l is not encouraged as it is hard to read so I had to go with ell. If some of the NumPyro devs have another suggestion I am open 🙂

[fehiepsi]

Thanks @juanitorduz for this great contribution! Thanks @omarfsosa and @martinjankowiak for reviewing! :)