Inverse Covariance Estimation for High-Dimensional Data in Linear Time and Space: Spectral Methods for Riccati and Sparse Models

@article{Honorio2013InverseCE,
  title={Inverse Covariance Estimation for High-Dimensional Data in Linear Time and Space: Spectral Methods for Riccati and Sparse Models},
  author={Jean Honorio and Tommi S. Jaakkola},
  journal={ArXiv},
  year={2013},
  volume={abs/1309.6838}
}
We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our optimization problem leads to a Riccati matrix equation, which has a closed form solution. We propose an efficient algorithm that performs a singular value decomposition of the training data. Our algorithm is O(NT^2)-time and O(NT)-space for N variables and T… CONTINUE READING
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