Abstract

This tutorial provides a comprehensive guide on leveraging the OTT-JAX toolbox to implement concepts derived from the Entropic Estimation of Optimal Transport Maps (EOT) [1]. Beginning with a detailed exploration of the mathematical foundations, this tutorial amalgamates insights from both EOT and Computational optimal transport (COT) [2] to show how to estimate the entropic estimator of the optimal transport map. Starting with a theoretical grounding, the tutorial progresses to demonstrate the application of this method on simulated data, showcasing convergence towards the true transport map. Furthermore, it extends this application to real seismic data, providing practical insights into estimating the entropic estimator for an actual earthquake dataset.

Collaborators

This work has been done in a group work with Arthur Katossky and Hélène Rondey , under the supervision of Marco Cuturi from Apple as part of the Optimal Transport course at ENSAE Paris.

References

[1] Pooladian, A.-A., & Niles-Weed, J. (2022). Entropic estimation of optimal transport maps.

[2] Peyré, G., & Cuturi, M. (2020). Computational Optimal Transport.