Free-Support Wasserstein-2 Barycenters

Implementations of the algorithms from the paper Simple Approximative Algorithms for Free-Support Wasserstein Barycenters (von Lindheim, 2022). For algorithms for the related multi-marginal optimal transport problem, see this repository.

Using the emd OT solver from the Python Optimal Transport (POT) package, which is a wrapper of this network simplex solver, which, in turn, is based on an implementation in the LEMON C++ library.

Installation

1. Download the code or clone the Github repository with

git clone https://github.com/jvlindheim/free-support-barycenters.git

2. For the code in bary.py, there is the following dependencies: numpy, matplotlib.pyplot, the cdist function from scipy.spatial.distance and the emd function from the POT library. You can install them e.g. using pip via

pip install --user numpy scipy matplotlib POT

If you want to run the demo notebook, you will also need to have Jupyter Notebook or JupyterLab installed.