Polyatomic Frank-Wolfe for the LASSO

This repository provides the code to run and reproduce the results for the IEEE Signal Processing Letters paper "A Fast and Scalable Polyatomic Frank-Wolfe Algorithm for the LASSO", from Adrian Jarret, Julien Fageot and Matthieu Simeoni.

The implementation is based on the optimization package Pycsou.

Installation

The code has been developed and tested on x86_64 systems running Linux, with Python 3.9.

Dependencies

The notebook extra dependencies are listed in the file requirements.txt. It is recommended to install those extra dependencies in an Anaconda environment Miniconda or Anaconda.

>> git clone https://github.com/AdriaJ/PolyatomicFW_SPL
>> cd PolyatomicFW_SPL/
>> conda create -n pfw python=3.9
>> conda activate pfw
>> pip install -r requirements.txt

Run the code

Once the dependencies installed and the environment activated, you can run reconstructions with PFW and compare them with the provided baselines (FISTA, Vanilla FW, Fully-Corrective FW). A testcase on a simulated sparse problem is showcased in the code example.py. In particular, we encourage you to try this code and play with the different parameters, especially n_sources (the sparsity index K from the article) and alpha.

>> python example.py

The following figure is an example of what can be obtained with different parameters.

In order to reproduce the plots of the paper, you should run the code plot_comparison_cs.py. This code will create 6 subplots similar to the ones provided in the paper (warning: it can be relatively long to run).

>> python plot_comparison_cs.py

The exact results of the paper are stored in the Pickle file results.p and can be plotted with

>> python plot_saved_results.py