5 papers
Minimax Private Estimation of Smooth Optimal-Transport Maps
Clément Lalanne, David Rodríguez-Vítores, Franck Iutzeler +1
We study the problem of estimating smooth optimal transport (OT) maps between two probability distributions under differential privacy (DP) constraints. Leveraging wavelet-based de…
Distributional Limit Theory for Optimal Transport
Eustasio del Barrio, Alberto González-Sanz, Jean-Michel Loubes +1
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitione…
An improved central limit theorem for the empirical sliced Wasserstein distance
David Rodríguez-Vítores, Eustasio del Barrio, Jean-Michel Loubes
Wasserstein distances are widely used in modern data analysis but pose significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance alle…
Learning with Differentially Private (Sliced) Wasserstein Gradients
David Rodríguez-Vítores, Clément Lalanne, Jean-Michel Loubes
In this work, we introduce a novel framework for privately optimizing objectives that rely on Wasserstein distances between data-dependent empirical measures. Our main theoretical…
Improving Model Choice in Classification: An Approach Based on Clustering of Covariance Matrices
David Rodríguez-Vítores, Carlos Matrán
This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance mat…