kose-y/minkowskiprojection

Companion website for "Projection onto Minkowski Sums with Application to Constrained Learning" (ICML 2019)

Supplementary materials for "Projection onto Minkowski Sums with Application to Constrained Learning" to appear in ICML 2019 by Kenneth Lange, Joong-Ho Won, 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