2024 : Manuscript of my thesis called "Unbalanced and Linear Optimal Transport for Reliable Estimation of the Wasserstein Distance". I defended my thesis the 13th of November. Here a quick summary:
In the context of machine learning, several problems can be formulated as distribution comparison problems. The mathematical theory of optimal transport allows for a comparison between two probability measures. Although very elegant in theory, optimal transport (OT) suffers from several practical drawbacks, notably the computational burden, the risk of overfitting, and its sensitivity to artifacts of sampling. All of this has motivated the introduction of variants to the loss function associated with OT in the machine learning community. In this thesis, we propose such variants in order, on one hand, to reduce the computational and statistical burden and, on the other hand, the sensitivity to sampling artifacts of the OT loss. To achieve this, we relied on intermediate distributions introduced by both the linear OT and unbalanced OT variants.
You can found the complete manuscript here.
2023 : Accepted Spotlight article at Neurips: "Fast Optimal Transport through Sliced Wasserstein Generalized Geodesics". This is joint work with Laetitia Chapel, Gilles Gasso, Clément Bonet and Nicolas Courty.
In this article we present a new proxy, called SWGG, for the Wasserstein distance, based on the 1D formulation of OT. In contrary to Sliced OT, SWGG provides a transport.
2024 : A kernel based penalization for the Unbalanced Optimal Transport. This is joint work with Felipe Tobar, Laetitia Chapel and Gilles Gasso.
In this article we proposed a Kernel version of the Kullback-Leibler divergence as a penalization for the Unbalanced Optimal Transport. We show that incorporating geometric information in the penalization mights benefit the Unbalanced Optimal Transport formulation in several classical applications.
2024 : Rebalanced optimal transportation: A Wasserstein penalty for unbalanced OT. This is joint work with Felipe Tobar, Laetitia Chapel and Gilles Gasso.
In this article we proposed a Wasserstein distance for the Unbalanced Optimal Transport formulation. This penalisation takes into account the geometry of the marginal and produces a hierarchy through the obtained transport plans.
2024 : Presentation of my current work in Unbalanced OT in the summer school: "Numerical methods for optimal transport problems, mean field games, and multi-agent dynamics".
2023 : Poster at Neurips for the article "Fast Optimal Transport through Sliced Wasserstein Generalized Geodesics".
2023 : Presentation of my article "Fast Optimal Transport through Sliced Wasserstein Generalized Geodesics" at the Probability seminar of Universidade de Chile.
All the code of my works is available at my Github. For any questions/requests feel free to mail me.