Vector-valued GPs

[emsal0]

Forgive me if it's already supported and I just missed it.

I can't seem to find anything in this library for vector-valued GPs as described in Section 3.3 of this paper. Are there plans to support it or is there a way to use them with the current functionality?

[maximerischard]

Not at the moment, see #113. This is definitely something we would like the package to support, but nobody has picked up this project yet.

[emsal0]

I can work on implementing at least the start of this project, as there's been interest in doing this for applications like in this issue in DiffEqBayes. I'll come up with a short proposal for an implementation plan soon?

[thomaspinder]

If you wanted to start on implementing the kernels required for a vector-valued GP, @emsal1863 that would be fantastic. I'd be happy to support if there's anything you run into trouble with.

A proposal would be great.

[emsal0]

Thanks for the support @thomaspinder, I'm a bit new to developing Julia packages so I've been learning the workflow as I go along looking at this. I've begun to look through the package and here's my initial general idea for how to implement this:

• The overall end-goal here is to make the GPA struct support having y as a type deriving from AbstractMatrix rather than just AbstractVector. In this commit on my branch I began starting to extend the functionality of the GPA class and to my surprise most of the functionality still works; there are still a couple of tests failing in the Optim test set though.
• To support y being an AbstractMatrix there would then need to be support for Mean types that return vector values. In order to maintain the current scalar-valued mean functions to continue working, I suggest that a good way to start out doing this is to make the library throw an "unsupported" error when trying to use one of the existing mean functions when using a y value that doesn't derive AbstractVector (can this be done?), then add new vector-valued Mean implementations. These could start out as vector-valued versions of the ones that currently exist like mLin, mPoly, etc.
• It seems that support for vector-valued samples (x) are already supported for the case of vector -> scalar functions, so (correct me if I'm wrong) I don't think anything needs to be added for the kernels.

Does my assessment seem correct?

Also, I'm still looking at the optimization and sampling methods and I don't really know how to assess the work that needs to be done there yet - can I get some help in understanding how these might need to be changed?

I'll continue trying to fix the issue with the Optim tests in the meantime.