6 papers
Convergence Rates for Distribution Matching with Sliced Optimal Transport
Gauthier Thurin, Claire Boyer, Kimia Nadjahi
We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution…
Monge-Kantorovich quantiles and ranks for image data
Gauthier Thurin
This paper defines quantiles, ranks and statistical depths for image data by leveraging ideas from measure transportation. The first step is to embed a distribution of images in a…
Optimal Transport-based Conformal Prediction
Gauthier Thurin, Kimia Nadjahi, Claire Boyer
Conformal Prediction (CP) is a principled framework for quantifying uncertainty in blackbox learning models, by constructing prediction sets with finite-sample coverage guarantees.…
Regularized estimation of Monge-Kantorovich quantiles for spherical data
Bernard Bercu, Jérémie Bigot, Gauthier Thurin
Tools from optimal transport (OT) theory have recently been used to define a notion of quantile function for directional data. In practice, regularization is mandatory for applicat…
Monge-Kantorovich superquantiles and expected shortfalls with applications to multivariate risk measurements
Bernard Bercu, Jeremie Bigot, Gauthier Thurin
We propose center-outward superquantile and expected shortfall functions, with applications to multivariate risk measurements, extending the standard notion of value at risk and co…
Stochastic optimal transport in Banach Spaces for regularized estimation of multivariate quantiles
Bernard Bercu, Jérémie Bigot, Gauthier Thurin
We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures and . Our work is motivated by th…