Multivariate generalized Gaussian distribution: Convexity and graphical models

Teng Zhang, Ami Wiesel, Maria Sabrina Greco

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been proved that its global solution can be often computed via simple fixed point iterations. Our first contribution is a new analysis of this likelihood based on geodesic convexity that requires weaker assumptions. Our second contribution is a generalized framework for structured covariance estimation under sparsity constraints. We show that the optimizations can be formulated as convex minimization as long the MGGD shape parameter is larger than half and the sparsity pattern is chordal. These include, for example, maximum likelihood estimation of banded inverse covariances in multivariate Laplace distributions, which are associated with time varying autoregressive processes.

Original languageAmerican English
Article number6530654
Pages (from-to)4141-4148
Number of pages8
JournalIEEE Transactions on Signal Processing
Issue number16
StatePublished - 2013


  • Cholesky decomposition
  • geodesic convexity
  • graphical models
  • multivariate generalized Gaussian distribution


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