From 5eedb5e3076fbe6ba29981ceca8839d852058b82 Mon Sep 17 00:00:00 2001 From: Aki Vehtari Date: Fri, 24 May 2024 19:39:48 +0300 Subject: [PATCH] warn about the computation cost of GPs --- src/bibtex/all.bib | 9 +++++++++ src/stan-users-guide/gaussian-processes.qmd | 10 ++++++++++ 2 files changed, 19 insertions(+) diff --git a/src/bibtex/all.bib b/src/bibtex/all.bib index 601a9eb29..eda4bd035 100644 --- a/src/bibtex/all.bib +++ b/src/bibtex/all.bib @@ -1816,3 +1816,12 @@ @article{zhang_pathfinder:2022 url = {http://jmlr.org/papers/v23/21-0889.html} } +@article{Riutort-Mayol:2023:HSGP, + title={Practical {Hilbert} space approximate {Bayesian} {Gaussian} processes for probabilistic programming}, + author={Riutort-Mayol, Gabriel and B{\"u}rkner, Paul-Christian and Andersen, Michael R and Solin, Arno and Vehtari, Aki}, + journal={Statistics and Computing}, + volume={33}, + number={1}, + pages={17}, + year={2023} +} diff --git a/src/stan-users-guide/gaussian-processes.qmd b/src/stan-users-guide/gaussian-processes.qmd index d8f636013..156968971 100644 --- a/src/stan-users-guide/gaussian-processes.qmd +++ b/src/stan-users-guide/gaussian-processes.qmd @@ -44,6 +44,16 @@ Gaussian processes are general, and by necessity this chapter only touches on some basic models. For more information, see @RasmussenWilliams:2006. +Note that fitting Gaussian processes as described below using exact +inference by computing Cholesky of the covariance matrix scales +cubicly with the size of data. Due to how Stan autodiff is +implemented, Stan is also slower than Gaussian process specialized +software. It is likely that Gaussian processes using exact inference +by computing Cholesky of the covariance matrix with $N>1000$ are too +slow for practical purposes in Stan. There are many approximations to +speed-up Gaussian process computation, from which the basis function +approaches for 1-3 dimensional $x$ are easiest to implement in Stan +(see, e.g., @Riutort-Mayol:2023:HSGP). ## Gaussian process regression