# Sparse Convolved Gaussian Processes for Multi-output Regression

Mauricio A. Álvarez, Universidad Tecnológica de Pereira, Colombia
Neil D. Lawrence, University of Sheffield

in Advances in Neural Information Processing Systems 21, pp 57-64

#### Abstract

We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network.

  @InProceedings{alvarez-convolved08, title = {Sparse Convolved Gaussian Processes for Multi-output Regression}, author = {Mauricio A. Álvarez and Neil D. Lawrence}, booktitle = {Advances in Neural Information Processing Systems}, pages = {57}, year = {2009}, editor = {Daphne Koller and Dale Schuurmans and Yoshua Bengio and Leon Bottou}, volume = {21}, address = {Cambridge, MA}, month = {00}, publisher = {MIT Press}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2009-01-01-alvarez-convolved08.md}, url = {http://inverseprobability.com/publications/alvarez-convolved08.html}, abstract = {We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network.}, crossref = {Koller:nips08}, key = {Alvarez:convolved08}, linkpdf = {ftp://ftp.dcs.shef.ac.uk/home/neil/spmulti.pdf}, linksoftware = {https://github.com/SheffieldML/multigp/}, OPTgroup = {} }
 %T Sparse Convolved Gaussian Processes for Multi-output Regression %A Mauricio A. Álvarez and Neil D. Lawrence %B %C Advances in Neural Information Processing Systems %D %E Daphne Koller and Dale Schuurmans and Yoshua Bengio and Leon Bottou %F alvarez-convolved08 %I MIT Press %P 57--64 %R %U http://inverseprobability.com/publications/alvarez-convolved08.html %V 21 %X We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network. 
 TY - CPAPER TI - Sparse Convolved Gaussian Processes for Multi-output Regression AU - Mauricio A. Álvarez AU - Neil D. Lawrence BT - Advances in Neural Information Processing Systems PY - 2009/01/01 DA - 2009/01/01 ED - Daphne Koller ED - Dale Schuurmans ED - Yoshua Bengio ED - Leon Bottou ID - alvarez-convolved08 PB - MIT Press SP - 57 EP - 64 L1 - ftp://ftp.dcs.shef.ac.uk/home/neil/spmulti.pdf UR - http://inverseprobability.com/publications/alvarez-convolved08.html AB - We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network. ER - 
 Álvarez, M.A. & Lawrence, N.D.. (2009). Sparse Convolved Gaussian Processes for Multi-output Regression. Advances in Neural Information Processing Systems 21:57-64