GGLasso -- a Python package for General Graphical Lasso computation

TL;DR

GGLasso is a Python package that efficiently solves various forms of the General Graphical Lasso problem, enabling sparse inverse covariance estimation for multivariate Gaussian data with extensions for latent variables and multiple matrices.

Contribution

It introduces a versatile Python package that implements algorithms for the General Graphical Lasso, covering several important variants and extensions in covariance estimation.

Findings

Provides a comprehensive implementation for multiple Graphical Lasso variants

Enables efficient sparse inverse covariance matrix estimation

Supports extensions including latent variables and joint estimation

Abstract

We introduce GGLasso, a Python package for solving General Graphical Lasso problems. The Graphical Lasso scheme, introduced by (Friedman 2007) (see also (Yuan 2007; Banerjee 2008)), estimates a sparse inverse covariance matrix $\Theta$ from multivariate Gaussian data $\mathcal{X} \sim \mathcal{N}(\mu, \Sigma) \in \mathbb{R}^p$. Originally proposed by (Dempster 1972) under the name Covariance Selection, this estimation framework has been extended to include latent variables in (Chandrasekaran 2012). Recent extensions also include the joint estimation of multiple inverse covariance matrices, see, e.g., in (Danaher 2013; Tomasi 2018). The GGLasso package contains methods for solving a general problem formulation, including important special cases, such as, the single (latent variable) Graphical Lasso, the Group, and the Fused Graphical Lasso.