Sparse Convolved Multiple Output Gaussian Processes

Mauricio A. ÁlvarezNeil D. Lawrence
, 2009.

Abstract

Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semi-definite, captures the dependencies between all the data points and across all the outputs. One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different sparse approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in pollution prediction, school exams score prediction and gene expression data.

Cite this Paper


BibTeX
@InProceedings{pmlr-v-alvarez-multitech09, title = {Sparse Convolved Multiple Output Gaussian Processes}, author = {Mauricio A. Álvarez and Neil D. Lawrence}, year = {}, editor = {}, url = {http://inverseprobability.com/publications/alvarez-multitech09.html}, abstract = {Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semi-definite, captures the dependencies between all the data points and across all the outputs. One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different sparse approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in pollution prediction, school exams score prediction and gene expression data.} }
Endnote
%0 Conference Paper %T Sparse Convolved Multiple Output Gaussian Processes %A Mauricio A. Álvarez %A Neil D. Lawrence %B %C Proceedings of Machine Learning Research %D %E %F pmlr-v-alvarez-multitech09 %I PMLR %J Proceedings of Machine Learning Research %P -- %U http://inverseprobability.com %V %W PMLR %X Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semi-definite, captures the dependencies between all the data points and across all the outputs. One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different sparse approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in pollution prediction, school exams score prediction and gene expression data.
RIS
TY - CPAPER TI - Sparse Convolved Multiple Output Gaussian Processes AU - Mauricio A. Álvarez AU - Neil D. Lawrence BT - PY - DA - ED - ID - pmlr-v-alvarez-multitech09 PB - PMLR SP - DP - PMLR EP - L1 - UR - http://inverseprobability.com/publications/alvarez-multitech09.html AB - Recently there has been an increasing interest in methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semi-definite, captures the dependencies between all the data points and across all the outputs. One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different sparse approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in pollution prediction, school exams score prediction and gene expression data. ER -
APA
Álvarez, M.A. & Lawrence, N.D.. (). Sparse Convolved Multiple Output Gaussian Processes. , in PMLR :-

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