FMGL: a MATLAB package for Fused Multiple Graphical Lasso

Yangjing Zhang, Ning Zhang, Defeng Sun, Kim-Chuan Toh

The software was first released on September 2020.
The software is designed to solve fused multiple graphical lasso (FMGL) problems of the following form given input data \(S=(S^{(1)},\ldots,S^{(L)})\)
\min\Big\{ \sum_{l=1}^L  \Big(-\log {\rm det} \Theta^{(l)} + \langle S^{(l)}, \Theta^{(l)} \rangle\Big) + P(\Theta)\mid \Theta = \big(\Theta^{(1)},\ldots,\Theta^{(L)}\big)\in
\mathbb{S}^p\times \cdots\times \mathbb{S}^p\Big\}
where \(
P(\Theta) = \lambda_1\,\sum_{l=1}^L \sum_{i\not=j} \left| \Theta^{(l)}_{ij}\right| + \lambda_2\,\sum_{l=2}^L \sum_{i\not=j}\left| \Theta^{(l)}_{ij} – \Theta^{(l-1)}_{ij} \right|
and \(\lambda_1\) and \(\lambda_2\) are positive regularization parameters. The dual problem is given by
-\min \Big\{\sum_{l=1}^{L} ( -\log{\rm det}(X^{(l)}) – p ) + P^*(X-S) \mid X=(X^{(1)},\ldots,X^{(L)})\Big\}
where \(P^*(\cdot)\) denotes the conjugate function of \(P\).

Solver: FMGL_PPA.m

Important note: this is a research software. It is not intended nor designed to be a general purpose software at the moment.

  1. N. Zhang, Y.J. Zhang, D.F. Sun, and K.C. Toh, An efficient linearly convergent regularized proximal point algorithm for fused multiple graphical Lasso problems, arXiv:1902.06952

Copyright: This version of FMGL is distributed under the  BSD 3-clause License.

Download here:
Please read. Welcome to FMGL-0!
  • Firstly, unpack the software.
  • Run Matlab in the directory FMGL-0.
  • After that, to see whether you have installed FMGL-0 correctly, type:
    >> startup
    >> test_FMGL
  • By now, FMGL is ready for you to use.