Adaptive Cholesky Gaussian Processes

Research output: Contribution to journalConference articleResearchpeer-review

Standard

Adaptive Cholesky Gaussian Processes. / Bartels, Simon; Stensbo-Smidt, Kristoffer; Moreno-Muñoz, Pablo; Boomsma, Wouter; Frellsen, Jes; Hauberg, Søren.

In: Proceedings of Machine Learning Research, Vol. 206, 2023, p. 408--452.

Research output: Contribution to journalConference articleResearchpeer-review

Harvard

Bartels, S, Stensbo-Smidt, K, Moreno-Muñoz, P, Boomsma, W, Frellsen, J & Hauberg, S 2023, 'Adaptive Cholesky Gaussian Processes', Proceedings of Machine Learning Research, vol. 206, pp. 408--452. <https://proceedings.mlr.press/v206/bartels23a.html>

APA

Bartels, S., Stensbo-Smidt, K., Moreno-Muñoz, P., Boomsma, W., Frellsen, J., & Hauberg, S. (2023). Adaptive Cholesky Gaussian Processes. Proceedings of Machine Learning Research, 206, 408--452. https://proceedings.mlr.press/v206/bartels23a.html

Vancouver

Bartels S, Stensbo-Smidt K, Moreno-Muñoz P, Boomsma W, Frellsen J, Hauberg S. Adaptive Cholesky Gaussian Processes. Proceedings of Machine Learning Research. 2023;206:408--452.

Author

Bartels, Simon ; Stensbo-Smidt, Kristoffer ; Moreno-Muñoz, Pablo ; Boomsma, Wouter ; Frellsen, Jes ; Hauberg, Søren. / Adaptive Cholesky Gaussian Processes. In: Proceedings of Machine Learning Research. 2023 ; Vol. 206. pp. 408--452.

Bibtex

@inproceedings{cce637ecd86049fbaa216c15435e4caf,
title = "Adaptive Cholesky Gaussian Processes",
abstract = "We present a method to approximate Gaussian process regression models to large datasets by considering only a subset of the data. Our approach is novel in that the size of the subset is selected on the fly during exact inference with little computational overhead. From an empirical observation that the log-marginal likelihood often exhibits a linear trend once a sufficient subset of a dataset has been observed, we conclude that many large datasets contain redundant information that only slightly affects the posterior. Based on this, we provide probabilistic bounds on the full model evidence that can identify such subsets. Remarkably, these bounds are largely composed of terms that appear in intermediate steps of the standard Cholesky decomposition, allowing us to modify the algorithm to adaptively stop the decomposition once enough data have been observed. ",
author = "Simon Bartels and Kristoffer Stensbo-Smidt and Pablo Moreno-Mu{\~n}oz and Wouter Boomsma and Jes Frellsen and S{\o}ren Hauberg",
year = "2023",
language = "English",
volume = "206",
pages = "408----452",
journal = "Proceedings of Machine Learning Research",
issn = "2640-3498",
note = "26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 ; Conference date: 25-04-2023 Through 27-04-2023",

}

RIS

TY - GEN

T1 - Adaptive Cholesky Gaussian Processes

AU - Bartels, Simon

AU - Stensbo-Smidt, Kristoffer

AU - Moreno-Muñoz, Pablo

AU - Boomsma, Wouter

AU - Frellsen, Jes

AU - Hauberg, Søren

PY - 2023

Y1 - 2023

N2 - We present a method to approximate Gaussian process regression models to large datasets by considering only a subset of the data. Our approach is novel in that the size of the subset is selected on the fly during exact inference with little computational overhead. From an empirical observation that the log-marginal likelihood often exhibits a linear trend once a sufficient subset of a dataset has been observed, we conclude that many large datasets contain redundant information that only slightly affects the posterior. Based on this, we provide probabilistic bounds on the full model evidence that can identify such subsets. Remarkably, these bounds are largely composed of terms that appear in intermediate steps of the standard Cholesky decomposition, allowing us to modify the algorithm to adaptively stop the decomposition once enough data have been observed.

AB - We present a method to approximate Gaussian process regression models to large datasets by considering only a subset of the data. Our approach is novel in that the size of the subset is selected on the fly during exact inference with little computational overhead. From an empirical observation that the log-marginal likelihood often exhibits a linear trend once a sufficient subset of a dataset has been observed, we conclude that many large datasets contain redundant information that only slightly affects the posterior. Based on this, we provide probabilistic bounds on the full model evidence that can identify such subsets. Remarkably, these bounds are largely composed of terms that appear in intermediate steps of the standard Cholesky decomposition, allowing us to modify the algorithm to adaptively stop the decomposition once enough data have been observed.

M3 - Conference article

VL - 206

SP - 408

EP - 452

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

SN - 2640-3498

T2 - 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023

Y2 - 25 April 2023 through 27 April 2023

ER -

ID: 344671585