# Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models

arXiv: https://arxiv.org/abs/1304.3206 · HTML: https://mlsanity.com/paper/1304.3206/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2013.

## Built on by (most cited first, 6 of 6)

- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [The Fisher-Rao geometry of CES distributions](https://mlsanity.com/paper/2310.01032/) (2023)
- [Low-complexity subspace-descent over symmetric positive definite manifold](https://mlsanity.com/paper/2305.02041/) (2023)
- [Energy-Tweedie: Score meets Score, Energy meets Energy](https://mlsanity.com/paper/2512.23818/) (2025)
- [Convex Parameter Estimation of Perturbed Multivariate Generalized Gaussian Distributions](https://mlsanity.com/paper/2312.07479/) (2023)
- [Statistical Analysis of using the Shapley Value for Sensor Anomaly Localization with Accurate Classifiers](https://mlsanity.com/paper/2606.00867/) (2026)

## Abstract (arXiv)

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.