Efficient Inference in Matrix-Variate Gaussian Models with i.i.d. Observation Noise

Oliver Stegle; Christoph Lippert; Joris Mooij; Neil D. Lawrence; Karsten Borgwardt

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Efficient Inference in Matrix-Variate Gaussian Models with i.i.d. Observation Noise

Oliver Stegle, Christoph Lippert, Joris Mooij, Neil D. Lawrence, Karsten Borgwardt

Neural Information Processing Systems:630-638, 2011.

Abstract

Inference in matrix-variate Gaussian models has major applications for multi- output prediction and joint learning of row and column covariances from matrix- variate data. Here, we discuss an approach for efficient inference in such models that explicitly account for iid observation noise. Computational
tractability can be retained by exploiting the Kronecker product between row and column covariance matrices. Using this framework, we show how to generalize the Graphical Lasso in order to learn a sparse inverse covariance between features while accounting for a low-rank confounding covariance between samples. We show practical utility on applications to biology, where we model covariances with more than 100,000 dimensions. We find greater accuracy in recovering biological network structures and are able to better reconstruct the confounders.

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Cite this Paper

BibTeX


@InProceedings{Stegle-sparse11,
  title = 	 {Efficient Inference in Matrix-Variate {G}aussian Models with i.i.d. Observation Noise},
  author = 	 {Stegle, Oliver and Lippert, Christoph and Mooij, Joris and Lawrence, Neil D. and Borgwardt, Karsten},
  booktitle = 	 {Neural Information Processing Systems},
  pages = 	 {630--638},
  year = 	 {2011},
  pdf = 	 {https://proceedings.neurips.cc/paper/2011/file/a732804c8566fc8f498947ea59a841f8-Paper.pdf},
  url = 	 {/publications/stegle-sparse11.html},
  abstract = 	 {Inference in matrix-variate Gaussian models has major applications for multi- output prediction and 
joint learning of row and column covariances from matrix- variate data. Here, we discuss an approach for 
efficient inference in such models that explicitly account for iid observation noise. Computational   
tractability can be retained by exploiting the Kronecker product between row and column covariance 
matrices. Using this framework, we show how to generalize the Graphical Lasso in order to learn a sparse 
inverse covariance between features while accounting for a low-rank confounding covariance between 
samples. We show practical utility on applications to biology, where we model covariances with more than 
100,000 dimensions. We find greater accuracy in recovering biological network structures and are able to 
better reconstruct the confounders.
}
}

Endnote

%0 Conference Paper
%T Efficient Inference in Matrix-Variate Gaussian Models with i.i.d. Observation Noise
%A Oliver Stegle
%A Christoph Lippert
%A Joris Mooij
%A Neil D. Lawrence
%A Karsten Borgwardt
%B Neural Information Processing Systems
%D 2011	
%F Stegle-sparse11
%P 630--638
%U /publications/stegle-sparse11.html
%X Inference in matrix-variate Gaussian models has major applications for multi- output prediction and 
joint learning of row and column covariances from matrix- variate data. Here, we discuss an approach for 
efficient inference in such models that explicitly account for iid observation noise. Computational   
tractability can be retained by exploiting the Kronecker product between row and column covariance 
matrices. Using this framework, we show how to generalize the Graphical Lasso in order to learn a sparse 
inverse covariance between features while accounting for a low-rank confounding covariance between 
samples. We show practical utility on applications to biology, where we model covariances with more than 
100,000 dimensions. We find greater accuracy in recovering biological network structures and are able to 
better reconstruct the confounders.

RIS


TY  - CPAPER
TI  - Efficient Inference in Matrix-Variate Gaussian Models with i.i.d. Observation Noise
AU  - Oliver Stegle
AU  - Christoph Lippert
AU  - Joris Mooij
AU  - Neil D. Lawrence
AU  - Karsten Borgwardt
BT  - Neural Information Processing Systems
DA  - 2011/12/12	
ID  - Stegle-sparse11
SP  - 630
EP  - 638
L1  - https://proceedings.neurips.cc/paper/2011/file/a732804c8566fc8f498947ea59a841f8-Paper.pdf
UR  - /publications/stegle-sparse11.html
AB  - Inference in matrix-variate Gaussian models has major applications for multi- output prediction and 
joint learning of row and column covariances from matrix- variate data. Here, we discuss an approach for 
efficient inference in such models that explicitly account for iid observation noise. Computational   
tractability can be retained by exploiting the Kronecker product between row and column covariance 
matrices. Using this framework, we show how to generalize the Graphical Lasso in order to learn a sparse 
inverse covariance between features while accounting for a low-rank confounding covariance between 
samples. We show practical utility on applications to biology, where we model covariances with more than 
100,000 dimensions. We find greater accuracy in recovering biological network structures and are able to 
better reconstruct the confounders.

ER  -

APA


Stegle, O., Lippert, C., Mooij, J., Lawrence, N.D. & Borgwardt, K.. (2011). Efficient Inference in Matrix-Variate Gaussian Models with i.i.d. Observation Noise. Neural Information Processing Systems:630-638 Available from /publications/stegle-sparse11.html.