Wasserstein Singular Vectors

wsingular is the Python package for the ICML 2022 paper “Unsupervised Ground Metric Learning Using Wasserstein Singular Vectors”.

Wasserstein Singular Vectors simultaneously compute a Wasserstein distance between samples and a Wasserstein distance between features of a dataset. These distance matrices emerge naturally as positive singular vectors of the function mapping ground costs to pairwise Wasserstein distances.

Get started

Install the package: pip install wsingular

Follow the tutorials in this documentation, and if you run into issue, leave an issue on the Github repo.

Tips

We strongly encourage torch.double precision for numerical stability.
You can easily run the demo notebook in Google Colab! Just use ‘open from Github’ and add !pip install wsingular at the beginning.
If you want to stop the computation of singular vectors early, just hit Ctrl-C and the function will return the result of the latest optimization step.

Citing us

The conference proceedings will be out soon. In the meantime you can cite our arXiv preprint.:

@article{huizing2021unsupervised,
  title={Unsupervised Ground Metric Learning using Wasserstein Eigenvectors},
  author={Huizing, Geert-Jan and Cantini, Laura and Peyr{\'e}, Gabriel},
  journal={arXiv preprint arXiv:2102.06278},
  year={2021}
}