The basic idea of learning a sparse full covariance for the Gaussian using Graphical models was proposed in the paper "Covaraince Selection".
In the paper "Sparse Gaussian Graphical Models for Speech Recognition", the authors adopted the sparse full covariance learning to speech recognition.
In the third paper, "Projected Subgradient Methods for Learning Sparse Gaussians", a new approach for estimating the covaraince is proposed.
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