Scalable Gaussian process inference

[tillahoffmann]

@fabio

I quickly read through the paper and I did not dig into the code. Is there a way to predict new data with functions like gp_*_cov_rfft2_rng ?

I have not implemented a gp_*_cov_rfft2_rng method yet. But one could probably use normal_rng together with the gp_inv_rfft2 transform transform to generate samples (see here for details).

Are you thinking of filling in missing values (e.g., interpolation), forecasting (e.g., in a time series setting), or a different problem? I can add something to the list of examples if of interest.

@avehtari

It would be nice to have guidance also which method to favor in comparison to Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming | SpringerLink, which is available in brms (although I’m co-author of that HSGP paper, I’m also happy if you can show the methods you implemented would always be favorable).

It looks like the main difference is the choice of boundary condition for the basis functions (Dirichlet in the linked paper and periodic with the FFT). But I need to read the Hilbert space approximation paper more carefully.

@avehtari

Tell my greetings to Jukka-Pekka!

Will do!

@pgree

A couple of collaborators and I just put out a paper on using Fourier representations for GP regression — [2210.10210] Equispaced Fourier representations for efficient Gaussian process regression from a billion data points . We generalize to non-equispaced data in 1, 2, 3 dimensions using the non-uniform FFT and have thus far implemented the algorithms in MATLAB.

Ah, I missed this one. I wasn’t aware of the non-equispaced fast Fourier transform and will have a look into your paper.

@pgree

We haven’t yet worked on any integration with Stan, but I think that would be a great future direction. It might also not require too much on top of all that you’ve already done. I think the main obstacle would be that there’s no non-uniform FFT in Stan. For our project we used Flatiron’s implementation — Flatiron Institute Nonuniform Fast Fourier Transform — finufft 2.1.0 documentation . They do have a C++ version, but I’m not sure what would be required to get that into Stan.

Getting the NUFFT into Eigen and then wrapping in Stan might be an option. But that is probably a more involved long-term project.