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Empirical Inference Conference Paper 2011

Efficient inference in matrix-variate Gaussian models with iid observation noise

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Empirical Inference
Joris Mooij
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Empirical Inference
Karsten Borgwardt

Inference in matrix-variate Gaussian models has major applications for multioutput prediction and joint learning of row and column covariances from matrixvariate 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.

Author(s): Stegle, O. and Lippert, C. and Mooij, J. and Lawrence, N. and Borgwardt, K.
Book Title: Advances in Neural Information Processing Systems 24
Pages: 630-638
Year: 2011
Day: 0
Editors: J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger
Bibtex Type: Conference Paper (inproceedings)
Event Name: Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS 2011)
Event Place: Granada, Spain
Digital: 0
Electronic Archiving: grant_archive
Links:

BibTex 

@inproceedings{StegleLMLB2012,
  title = {Efficient inference in matrix-variate Gaussian models with iid observation noise},
  booktitle = {Advances in Neural Information Processing Systems 24},
  abstract = {Inference in matrix-variate Gaussian models has major applications for multioutput prediction and joint learning of row and column covariances from matrixvariate 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.},
  pages = {630-638},
  editors = {J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger},
  year = {2011},
  slug = {steglelmlb2012},
  author = {Stegle, O. and Lippert, C. and Mooij, J. and Lawrence, N. and Borgwardt, K.}
}