This repository contains a Google Colab notebook demonstrating sparsity-constrained optimal transport, as proposed in our publication:
Liu, T., Puigcerver, J., & Blondel, M. (2023). Sparsity-constrained optimal transport. Proceedings of the Eleventh International Conference on Learning Representations (ICLR).
We focus on 1D problems here: transporting between 1D distributions. The official implementation in the vmoe repository includes additional demos showcasing applications in 2D, color transfer, and vision mixture-of-experts models.
While the official vmoe repository is based on JAX, this repository also demonstrates the usage of sparsity-constrained OT in PyTorch (thanks to the backend system in POT).
Optimal transport between two 1D Gaussians.
To try out the demo notebook, click the "Open in Colab" button above or access it here.
Please find more details in our paper, accepted for a spotlight presentation at ICLR 2023; if you find our work useful in your research, please consider citing:
@inproceedings{
liu2023sparsity,
title={Sparsity-constrained optimal transport},
author={Tianlin Liu, Joan Puigcerver, Mathieu Blondel},
booktitle={Proceedings of the Eleventh International Conference on Learning Representations (ICLR)},
year={2023},
url={https://openreview.net/forum?id=yHY9NbQJ5BP}
}