Supplementary materials for Projection onto Minkowski Sums with Application to Constrained Learning published in ICML 2019 by Joong-Ho Won, Kenneth Lange, and Jason Xu

Overview

• SLEP MATLAB toolbox (SLEP-master.zip)
  • MATLAB toolbox consisting of functions for sparse regression, especially the proximity operator for $\ell_{1,2}$-overlapping group lasso.
• SparseReg MATLAB toolbox (SparseReg-0.0.2.zip)
  • MATLAB toolbox consisting of functions for sparse regression, especially ADMM for constrained lasso.
• overlappinggroup subdirectory
  • Contains MATLAB code to reproduce the results in Section 4.1. See below for further details.
• constrainedlasso subdirectory
  • Contains MATLAB code to reproduce the results in Section 4.2. See below for further details.

Code & Data

Requirements

• MATLAB code
  • SLEP toolbox
    • Version 4.1 is included in these supplementary materials as a .zip file. This version of the toolbox can also be downloded from https://github.com/jiayuzhou/SLEP. The original link http://www.yelab.net/software/SLEP appears to be dead.
  • SparseReg toolbox
    • Version 0.0.2 is included in these supplementary materials as a .zip file. The latest version of the toolbox can be downloaded from https://github.com/Hua-Zhou/SparseReg
  • Gurobi optimization software
    • Gurobi can be downloaded from http://www.gurobi.com/
    • Free academic licenses are available
• MATLAB code
  • The overlappinggroup/ subdirectory contains five .m files. sim1.m is the main simulation loop. grplasso_prox.m is the Minkowski projection based code for computing proximity operator for the overlapping group lasso penalty. This code calls minkowski_proj.m, for which getLqDiskProjections.m provides the required projections to the summand sets. grpprox_obj.m computes the value of the objective function for the proximity operator (Moreau-Yosida smoothing).
  • The constrainedlasso/ subdirectory contains four .m files. sim1.m is the main simulation loop for the zero-sum constrained lasso. sim2.m is the main simulation loop for the nonnegative lasso. Both files call classo_proxgrad.m, which implements the proximal gradient descent for the constrained lasso based on the Minkowski projection. This in turn calls minkowski_proj.m. The required projections to the summands are hard-coded in sim1.m and sim2.m.

Simulations

• Make sure that Gurobi was installed successfully, and that the directories for the SparseReg toolbox and Gurobi have been added to MATLAB's search paths.

Acknowledgment

• This document and the simulation loops were modified from the Supplementary Material for "Algorithms for Fitting the Constrained Lasso" by Brian Gaines, Juhyun Kim and Hua Zhou, available at https://doi.org/10.1080/10618600.2018.1473777