Kronecker Graphical Lasso
MICHIGAN UNIV ANN ARBOR DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
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We consider high-dimensional estimation of a possibly sparse Kronecker-decomposable covariance matrix given i.i.d. Gaussian samples. We propose a sparse covariance estimation algorithm, the Kronecker Graphical Lasso KGlasso, for the high-dimensional setting that takes advantage of structure and sparsity. Convergence and limit point characterization of this iterative algorithm are established. Compared to standard Glasso, KGlasso has low computational complexity as the dimension of the covariance matrix increases. We derive a tight mean squared error MSE convergence rate for KGlasso and show that it outperforms standard Glasso and the flip-flop algorithm. Simulations validate these results and show that KGlasso outperforms the maximum-likelihood solution FF in the high-dimensional small-sample regime.
- Numerical Mathematics
- Statistics and Probability