Chained Gaussian Processes

Alan D. Saul; James Hensman; Aki Vehtari; Neil D. Lawrence

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Chained Gaussian Processes

Alan D. Saul, James Hensman, Aki Vehtari, Neil D. Lawrence

Proceedings of the Nineteenth International Workshop on Artificial Intelligence and Statistics, PMLR 51:1431-1440, 2016.

Abstract

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models “Chained Gaussian Processes”: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.

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Cite this Paper

BibTeX


@InProceedings{Saul-chained16,
  title = 	 {Chained {G}aussian Processes},
  author = 	 {Saul, Alan D. and Hensman, James and Vehtari, Aki and Lawrence, Neil D.},
  booktitle = 	 {Proceedings of the Nineteenth International Workshop on Artificial Intelligence and Statistics},
  pages = 	 {1431--1440},
  year = 	 {2016},
  editor = 	 {Gretton, Arthur and Robert, Cristian},
  volume = 	 {51},
  address = 	 {Cadiz, Spain},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v51/saul16.pdf},
  url = 	 {/publications/saul-chained16.html},
  abstract = 	 {Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models “Chained Gaussian Processes”: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.}
}

Endnote

%0 Conference Paper
%T Chained Gaussian Processes
%A Alan D. Saul
%A James Hensman
%A Aki Vehtari
%A Neil D. Lawrence
%B Proceedings of the Nineteenth International Workshop on Artificial Intelligence and Statistics
%D 2016
%E Arthur Gretton
%E Cristian Robert	
%F Saul-chained16
%I PMLR
%P 1431--1440
%U /publications/saul-chained16.html
%V 51
%X Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models “Chained Gaussian Processes”: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.

RIS


TY  - CPAPER
TI  - Chained Gaussian Processes
AU  - Alan D. Saul
AU  - James Hensman
AU  - Aki Vehtari
AU  - Neil D. Lawrence
BT  - Proceedings of the Nineteenth International Workshop on Artificial Intelligence and Statistics
DA  - 2016/05/02
ED  - Arthur Gretton
ED  - Cristian Robert	
ID  - Saul-chained16
PB  - PMLR
VL  - 51
SP  - 1431
EP  - 1440
L1  - http://proceedings.mlr.press/v51/saul16.pdf
UR  - /publications/saul-chained16.html
AB  - Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models “Chained Gaussian Processes”: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.
ER  -

APA


Saul, A.D., Hensman, J., Vehtari, A. & Lawrence, N.D.. (2016). Chained Gaussian Processes. Proceedings of the Nineteenth International Workshop on Artificial Intelligence and Statistics 51:1431-1440 Available from /publications/saul-chained16.html.