Debiased Sinkhorn barycenters

Guide to reproduce the results of (Janati et al, 2020, Debiased Sinkhorn barycenters) available at http://arxiv.org/abs/2006.02575. All experiments can be ran on CPU or GPUs. In the results reported in the paper, this is our used config with the computation time:

• Theorem illustrations + convergence plot (CPU) a few seconds
• Ellipses (CPU): 3 minutes
• Barycenters of 3D shapes (GPU): 15 seconds

• OT barycentric embedding: ot embedding on (GPU) (1h) + Random forest

  training on CPU (5 minutes)

All figures are saved in the fig/ folder.

Dependencies

Please make sure you have a miniconda environment installed and the following necessary dependencies (available through pip or conda):

• numpy
• matplotlib
• scikit-learn
• torch
• pandas

1. Ellipses Experiment

Moreover, to reproduce the Ellipse experiment, you will need:

1. to install the free support barycenter code of (G. Luise, 2019) that is shipped in the folder otbar. Inside the folder otbar, run: ```

python setup.py develop

```

2. to have an installed version of matlab 2019b to reproduce the MAAIPM barycenter of (Dongdong, 2019). And to install the Matlab engine API for Python. See https://fr.mathworks.com/help/matlab/matlab_external/install-the-matlab-engine-for-python.html

3. run python plot_ellipse_bar.py

2. Barycenters of 3D shapes

run python run_barycenter_3d.py run python plot_barycenter_3d.py

The images are saved in the fig/3d folder.

3. MNIST barycentric Encoding

run python run_ot_embedding.py run python run_random_forest.py run python plot_mnist_scores.py