Efficient Gaussian Process Inference for Short-Scale Spatio-Temporal Modeling

Jaakko Luttinen, Alexander Ilin
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:741-750, 2012.

Abstract

This paper presents an efficient Gaussian process inference scheme for modeling shortscale phenomena in spatio-temporal datasets. Our model uses a sum of separable, compactly supported covariance functions, which yields a full covariance matrix represented in terms of small sparse matrices operating either on the spatial or temporal domain. The proposed inference procedure is based on Gibbs sampling, in which samples from the conditional distribution of the latent function values are obtained by applying a simple linear transformation to samples drawn from the joint distribution of the function values and the observations. We make use of the proposed model structure and the conjugate gradient method to compute the required transformation. In the experimental part, the proposed algorithm is compared to the standard approach using the sparse Cholesky decomposition and it is shown to be much faster and computationally feasible for 100-1000 times larger datasets. We demonstrate the advantages of the proposed method in the problem of reconstructing sea surface temperature, which requires processing of a real-world dataset with 10^6 observations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-luttinen12, title = {Efficient Gaussian Process Inference for Short-Scale Spatio-Temporal Modeling}, author = {Luttinen, Jaakko and Ilin, Alexander}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {741--750}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/luttinen12/luttinen12.pdf}, url = {https://proceedings.mlr.press/v22/luttinen12.html}, abstract = {This paper presents an efficient Gaussian process inference scheme for modeling shortscale phenomena in spatio-temporal datasets. Our model uses a sum of separable, compactly supported covariance functions, which yields a full covariance matrix represented in terms of small sparse matrices operating either on the spatial or temporal domain. The proposed inference procedure is based on Gibbs sampling, in which samples from the conditional distribution of the latent function values are obtained by applying a simple linear transformation to samples drawn from the joint distribution of the function values and the observations. We make use of the proposed model structure and the conjugate gradient method to compute the required transformation. In the experimental part, the proposed algorithm is compared to the standard approach using the sparse Cholesky decomposition and it is shown to be much faster and computationally feasible for 100-1000 times larger datasets. We demonstrate the advantages of the proposed method in the problem of reconstructing sea surface temperature, which requires processing of a real-world dataset with 10^6 observations.} }
Endnote
%0 Conference Paper %T Efficient Gaussian Process Inference for Short-Scale Spatio-Temporal Modeling %A Jaakko Luttinen %A Alexander Ilin %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-luttinen12 %I PMLR %P 741--750 %U https://proceedings.mlr.press/v22/luttinen12.html %V 22 %X This paper presents an efficient Gaussian process inference scheme for modeling shortscale phenomena in spatio-temporal datasets. Our model uses a sum of separable, compactly supported covariance functions, which yields a full covariance matrix represented in terms of small sparse matrices operating either on the spatial or temporal domain. The proposed inference procedure is based on Gibbs sampling, in which samples from the conditional distribution of the latent function values are obtained by applying a simple linear transformation to samples drawn from the joint distribution of the function values and the observations. We make use of the proposed model structure and the conjugate gradient method to compute the required transformation. In the experimental part, the proposed algorithm is compared to the standard approach using the sparse Cholesky decomposition and it is shown to be much faster and computationally feasible for 100-1000 times larger datasets. We demonstrate the advantages of the proposed method in the problem of reconstructing sea surface temperature, which requires processing of a real-world dataset with 10^6 observations.
RIS
TY - CPAPER TI - Efficient Gaussian Process Inference for Short-Scale Spatio-Temporal Modeling AU - Jaakko Luttinen AU - Alexander Ilin BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-luttinen12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 741 EP - 750 L1 - http://proceedings.mlr.press/v22/luttinen12/luttinen12.pdf UR - https://proceedings.mlr.press/v22/luttinen12.html AB - This paper presents an efficient Gaussian process inference scheme for modeling shortscale phenomena in spatio-temporal datasets. Our model uses a sum of separable, compactly supported covariance functions, which yields a full covariance matrix represented in terms of small sparse matrices operating either on the spatial or temporal domain. The proposed inference procedure is based on Gibbs sampling, in which samples from the conditional distribution of the latent function values are obtained by applying a simple linear transformation to samples drawn from the joint distribution of the function values and the observations. We make use of the proposed model structure and the conjugate gradient method to compute the required transformation. In the experimental part, the proposed algorithm is compared to the standard approach using the sparse Cholesky decomposition and it is shown to be much faster and computationally feasible for 100-1000 times larger datasets. We demonstrate the advantages of the proposed method in the problem of reconstructing sea surface temperature, which requires processing of a real-world dataset with 10^6 observations. ER -
APA
Luttinen, J. & Ilin, A.. (2012). Efficient Gaussian Process Inference for Short-Scale Spatio-Temporal Modeling. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:741-750 Available from https://proceedings.mlr.press/v22/luttinen12.html.

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