Cross-Validation (pseudo-likelihood) Criterion

[evanmunro]

I am finding for a specific use case for Gaussian Process Regression that optimizing kernel hyperparameters using the marginal likelihood logpdf results in poor generalization.

I would like to try optimizing the kernel hyperparameters instead with respect to the pseudo-likelihood, Equation 5.11/5.12 in Rasmussen and Williams Chapter 5.

I'm happy to make an attempt at implementing this, but wondering if there have been any previous thoughts about doing this, or any suggestions on how to structure.

[willtebbutt]

Hi @evanmunro . I hadn't given any previous thought to implementing this, but an implementation would be welcome.

In terms of the implementing the objective function, I would suggest taking inspiration from https://github.com/willtebbutt/Stheno.jl/blob/68c4ce277ddc7284971232bf002d7e273a76039e/src/abstract_gp.jl#L197

and would actually recommend putting your implementation of the objective immediately below the compute_intermediates implementation in the same file. I would also recommend against using the gradient computations suggested in the textbook, and instead just rely on Zygote.

Very happy to review whatever you produce :)