Efficient Multioutput Gaussian Processes through Variational Inducing Kernels

Mauricio A. Álvarez, David Luengo, Michalis K. Titsias, Neil D. Lawrence
Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics, PMLR 9:25-32, 2010.

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 @Alvarez:convolved08 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 @Titsias:variational09 to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.

Cite this Paper

BibTeX
@InProceedings{Alvarez:efficient10, title = {Efficient Multioutput {G}aussian Processes through Variational Inducing Kernels}, author = {Álvarez, Mauricio A. and Luengo, David and Titsias, Michalis K. and Lawrence, Neil D.}, booktitle = {Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics}, pages = {25--32}, year = {2010}, editor = {Teh, Yee Whye and Titterington, D. Michael}, volume = {9}, address = {Chia Laguna Resort, Sardinia, Italy}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/alvarez10a/alvarez10a.pdf}, url = {http://inverseprobability.com/publications/alvarez-efficient10.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 @Alvarez:convolved08 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 @Titsias:variational09 to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.} }
Endnote
%0 Conference Paper %T Efficient Multioutput Gaussian Processes through Variational Inducing Kernels %A Mauricio A. Álvarez %A David Luengo %A Michalis K. Titsias %A Neil D. Lawrence %B Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics %D 2010 %E Yee Whye Teh %E D. Michael Titterington %F Alvarez:efficient10 %I PMLR %P 25--32 %U http://inverseprobability.com/publications/alvarez-efficient10.html %V 9 %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 @Alvarez:convolved08 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 @Titsias:variational09 to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and financial time series.
RIS
TY - CPAPER TI - Efficient Multioutput Gaussian Processes through Variational Inducing Kernels AU - Mauricio A. Álvarez AU - David Luengo AU - Michalis K. Titsias AU - Neil D. Lawrence BT - Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - D. Michael Titterington ID - Alvarez:efficient10 PB - PMLR VL - 9 SP - 25 EP - 32 L1 - http://proceedings.mlr.press/v9/alvarez10a/alvarez10a.pdf UR - http://inverseprobability.com/publications/alvarez-efficient10.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 @Alvarez:convolved08 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 @Titsias:variational09 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.. (2010). Efficient Multioutput Gaussian Processes through Variational Inducing Kernels. Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics 9:25-32 Available from http://inverseprobability.com/publications/alvarez-efficient10.html.

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