Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes

Mauricio A. Álvarez; David Luengo; Michalis K. Titsias; Neil D. Lawrence

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Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes

Mauricio A. Álvarez, David Luengo, Michalis K. Titsias, Neil D. Lawrence

, 2009.

Abstract

Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function over correlated output functions. One way of constructing such kernels is based on convolution processes (CP). A key problem for this approach is efficient inference. Álvarez and Lawrence (2009) recently presented a sparse approximation for CPs that enabled efficient inference. In this paper, we extend this work in two directions: we introduce the concept of variational inducing functions to handle potential non-smooth functions involved in the kernel CP construction and we consider an alternative approach to approximate inference based on variational methods, extending the work by Titsias (2009) to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.

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Cite this Paper

BibTeX


@Misc{Alvarez:vikTech09,
  title = 	 {Variational Inducing Kernels for Sparse Convolved Multiple Output {G}aussian Processes},
  author = 	 {Álvarez, Mauricio A. and Luengo, David and Titsias, Michalis K. and Lawrence, Neil D.},
  year = 	 {2009},
  pdf = 	 {https://arxiv.org/pdf/0912.3268.pdf},
  url = 	 {/publications/alvarez-viktech09.html},
  abstract = 	 {Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function over correlated output functions. One way of constructing such kernels is based on convolution processes (CP). A key problem for this approach is efficient inference. Álvarez and Lawrence (2009) recently presented a sparse approximation for CPs that enabled efficient inference. In this paper, we extend this work in two directions: we introduce the concept of variational inducing functions to handle potential non-smooth functions involved in the kernel CP construction and we consider an alternative approach to approximate inference based on variational methods, extending the work by Titsias (2009) to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.}
}

Endnote

%0 Generic
%T Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes
%A Mauricio A. Álvarez
%A David Luengo
%A Michalis K. Titsias
%A Neil D. Lawrence
%D 2009	
%F Alvarez:vikTech09
%U /publications/alvarez-viktech09.html
%X Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function over correlated output functions. One way of constructing such kernels is based on convolution processes (CP). A key problem for this approach is efficient inference. Álvarez and Lawrence (2009) recently presented a sparse approximation for CPs that enabled efficient inference. In this paper, we extend this work in two directions: we introduce the concept of variational inducing functions to handle potential non-smooth functions involved in the kernel CP construction and we consider an alternative approach to approximate inference based on variational methods, extending the work by Titsias (2009) to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.

RIS


TY  - GEN
TI  - Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes
AU  - Mauricio A. Álvarez
AU  - David Luengo
AU  - Michalis K. Titsias
AU  - Neil D. Lawrence
DA  - 2009/12/16	
ID  - Alvarez:vikTech09
L1  - https://arxiv.org/pdf/0912.3268.pdf
UR  - /publications/alvarez-viktech09.html
AB  - Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function over correlated output functions. One way of constructing such kernels is based on convolution processes (CP). A key problem for this approach is efficient inference. Álvarez and Lawrence (2009) recently presented a sparse approximation for CPs that enabled efficient inference. In this paper, we extend this work in two directions: we introduce the concept of variational inducing functions to handle potential non-smooth functions involved in the kernel CP construction and we consider an alternative approach to approximate inference based on variational methods, extending the work by Titsias (2009) to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.
ER  -

APA


Álvarez, M.A., Luengo, D., Titsias, M.K. & Lawrence, N.D.. (2009). Variational Inducing Kernels for Sparse Convolved Multiple Output Gaussian Processes.  Available from /publications/alvarez-viktech09.html.