Efficient Sampling for Gaussian Process Inference using Control Variables

Michalis K. Titsias; Neil D. Lawrence; Magnus Rattray

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Efficient Sampling for Gaussian Process Inference using Control Variables

Michalis K. Titsias, Neil D. Lawrence, Magnus Rattray

Advances in Neural Information Processing Systems, MIT Press 21:1681-1688, 2008.

Abstract

Sampling functions in Gaussian process (GP) models is challenging because of the highly correlated posterior distribution. We describe an efficient Markov chain Monte Carlo algorithm for sampling from the posterior process of the GP model. This algorithm uses control variables which are auxiliary function values that provide a low dimensional representation of the function. At each iteration, the algorithm proposes new values for the control variables and generates the function from the conditional GP prior. The control variable input locations are found by continuously minimizing an objective function. We demonstrate the algorithm on regression and classification problems and we use it to estimate the parameters of a differential equation model of gene regulation.

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BibTeX


@InProceedings{Titsias-efficient08,
  title = 	 {Efficient Sampling for {G}aussian Process Inference using Control Variables},
  author = 	 {Titsias, Michalis K. and Lawrence, Neil D. and Rattray, Magnus},
  booktitle = 	 {Advances in Neural Information Processing Systems},
  pages = 	 {1681--1688},
  year = 	 {2008},
  editor = 	 {Koller, Daphne and Schuurmans, Dale and Bengio, Yoshua and Bottou, Leon},
  volume = 	 {21},
  address = 	 {Cambridge, MA},
  publisher =    {MIT Press},
  pdf = 	 {https://proceedings.neurips.cc/paper/2008/file/5487315b1286f907165907aa8fc96619-Paper.pdf},
  url = 	 {/publications/titsias-efficient08.html},
  abstract = 	 {Sampling functions in Gaussian process (GP) models is challenging because of the highly correlated posterior distribution. We describe an efficient Markov chain Monte Carlo algorithm for sampling from the posterior process of the GP model. This algorithm uses control variables which are auxiliary function values that provide a low dimensional representation of the function. At each iteration, the algorithm proposes new values for the control variables and generates the function from the conditional GP prior. The control variable input locations are found by continuously minimizing an objective function. We demonstrate the algorithm on regression and classification problems and we use it to estimate the parameters of a differential equation model of gene regulation.}
}

Endnote

%0 Conference Paper
%T Efficient Sampling for Gaussian Process Inference using Control Variables
%A Michalis K. Titsias
%A Neil D. Lawrence
%A Magnus Rattray
%B Advances in Neural Information Processing Systems
%D 2008
%E Daphne Koller
%E Dale Schuurmans
%E Yoshua Bengio
%E Leon Bottou	
%F Titsias-efficient08
%I MIT Press
%P 1681--1688
%U /publications/titsias-efficient08.html
%V 21
%X Sampling functions in Gaussian process (GP) models is challenging because of the highly correlated posterior distribution. We describe an efficient Markov chain Monte Carlo algorithm for sampling from the posterior process of the GP model. This algorithm uses control variables which are auxiliary function values that provide a low dimensional representation of the function. At each iteration, the algorithm proposes new values for the control variables and generates the function from the conditional GP prior. The control variable input locations are found by continuously minimizing an objective function. We demonstrate the algorithm on regression and classification problems and we use it to estimate the parameters of a differential equation model of gene regulation.

RIS


TY  - CPAPER
TI  - Efficient Sampling for Gaussian Process Inference using Control Variables
AU  - Michalis K. Titsias
AU  - Neil D. Lawrence
AU  - Magnus Rattray
BT  - Advances in Neural Information Processing Systems
DA  - 2008/12/08
ED  - Daphne Koller
ED  - Dale Schuurmans
ED  - Yoshua Bengio
ED  - Leon Bottou	
ID  - Titsias-efficient08
PB  - MIT Press
VL  - 21
SP  - 1681
EP  - 1688
L1  - https://proceedings.neurips.cc/paper/2008/file/5487315b1286f907165907aa8fc96619-Paper.pdf
UR  - /publications/titsias-efficient08.html
AB  - Sampling functions in Gaussian process (GP) models is challenging because of the highly correlated posterior distribution. We describe an efficient Markov chain Monte Carlo algorithm for sampling from the posterior process of the GP model. This algorithm uses control variables which are auxiliary function values that provide a low dimensional representation of the function. At each iteration, the algorithm proposes new values for the control variables and generates the function from the conditional GP prior. The control variable input locations are found by continuously minimizing an objective function. We demonstrate the algorithm on regression and classification problems and we use it to estimate the parameters of a differential equation model of gene regulation.
ER  -

APA


Titsias, M.K., Lawrence, N.D. & Rattray, M.. (2008). Efficient Sampling for Gaussian Process Inference using Control Variables. Advances in Neural Information Processing Systems 21:1681-1688 Available from /publications/titsias-efficient08.html.