The GOPT toolbox contains functions for optimization over the manifold of PSD (HPD) matrices, as well as a collection of functions for computing maximum-likelihood estimates for Elliptical Gamma Distributions (EGDs) and calculating the KL-divergence between EGDs.

Please see the end of this README for a list of the algorithms available.

This toolbox is copyright (C) 2014 by Reshad Hosseini & Suvrit Sra and is distributed under the terms of the GNU General Public License (GPL) version 3 (or later).

Contact: Reshad Hosseini or Suvrit Sra

Quick installation guide

Directory structure

./ The top directory with README.md
 | mbfgs/           - Manifold BFGS
 | manifoldPSD/     - psd and hpd classes (use with manopt)
 | means-medians/   - algos for means and medians of PSD matrices
 | examples/        - some examples showing how to use GOPT
 | eg/              - algorithms specific to EGDs
 | kotz/            - algorithms specific to Kotz type distributions
 | ThirdParty/      - Third party tools
   |--- lightspeed/       - subset of Tom Minka's matlab toolbox
   |--- manopt/           - the manopt toolbox
   |--- prettyPlot/       - our version of Mark Schmidt's plot tools


If you find manifold LBFGS or the PSD (HPD) manifold useful in your work, please cite the following two papers:

  author  = {Suvrit Sra and Reshad Hosseini},
  title   = {Conic Geometric Optimisation on the Manifold of Positive Definite Matrices},
  journal = {SIAM Journal of Optimization},
  year    = {Under Review (2013)},
  note    = {arXiv:1312.1039v2}

  author  = {Nicolas Boumal and Bamdev Mishra and P.-A. Absil and Rodolphe Sepulchre},
  title   = {{M}anopt, a {M}atlab Toolbox for Optimization on Manifolds},
  journal = {Journal of Machine Learning Research},
  year    = {2014},
  volume  = {15},
  pages   = {1455--1459},
  url     = {http://www.manopt.org}

If you are using functions for estimating KL-divergence between EGDs or ML-estimation of parameters of EGD, please cite the following paper:

  author  = {Reshad Hosseini and Suvrit Sra and Lucas Theis and Matthias Bethge},
  title   = {Statistical Inference with the Elliptical Gamma Distribution},
  journal = {arXiv:1410.4812},
  year    = {2014},



Last updated Tue Jan 20 14:34:20 EST 2015