Jourdain, Benjamin Margheriti, William Pammer, Gudmund

Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one, it is well-known that the set of probability measures with a given mean is a lattice w.r.t. the convex order. O...

Klatt, M Munk, A Zemel, Y

Abstract
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. For the corresponding random linear program, we characterize under general assumptions the random fluctuations of the empirical optimal solutions around their population quantities after standardization by a dist...

Geniesse, Caleb Chowdhury, Samir Saggar, Manish
Published in
Network Neuroscience

Modern neuroimaging promises to transform how we understand human brain function, as well as how we diagnose and treat mental disorders. However, this promise hinges on the development of computational tools for distilling complex, high-dimensional neuroimaging data into simple representations that can be explored in research or clinical settings. ...

Golse, François Paul, Thierry

This paper proves variants of the triangle inequality for the quantum analogues of the Wasserstein metric of exponent 2 introduced in Golse et al. (2016) to compare two density operators, and in Golse and Paul (2017) to compare a phase space probability measure and a density operator. The argument differs noticeably from the classical proof of the ...

Liu, Shu

In this thesis we apply the optimal transport (OT) theory to various disciplines of applied and computational mathematics such as scientific computing, numerical analysis, and dynamical systems. The research consists of three aspects: (1) We focus on solving OT problems from different perspectives including (a) direct approximation of the OT map in...

Del Barrio, Eustasio González-Sanz, Alberto Hallin, Marc

Based on the novel concept of multivariate center-outward quantiles introduced recently in Chernozhukov et al. (2017) and Hallin et al. (2021), we are considering the problem of nonparametric multiple-output quantile regression. Our approach defines nested conditional center-outward quantile regression contours and regions with given conditional pr...

Staerman, Guillaume

Enthusiasm for Machine Learning is spreading to nearly all fields such as transportation, energy, medicine, banking or insurance as the ubiquity of sensors through IoT makes more and more data at disposal with an ever finer granularity. The abundance of new applications for monitoring of complex infrastructures (e.g. aircrafts, energy networks) tog...

Massri, Maria Miklos, Zoltan Raipin, Philippe Meye, Pierre

Graph management systems are emerging as an efficient solution to store and query graph-oriented data. To assess the performance and compare such systems, practitioners often design benchmarks in which they use large scale graphs. However, such graphs either do not fit the scale requirements or are not publicly available. This has been the incentiv...

Boyd, Alexander B. Patra, Ayoti Jarzynski, Christopher Crutchfield, James P.
Published in
Journal of Statistical Physics

Landauer’s Principle states that the energy cost of information processing must exceed the product of the temperature, Boltzmann’s constant, and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations—that is, only over infinite time. In...

Leclaire, Arthur Delon, Julie Desolneux, Agnès

Using optimal transport in image processing tasks has become very popular. However, it still faces difficult computational issues when dealing with high dimensional distributions. We propose here to use the recently introduced GMM-OT formulation, which consists in restricting the optimal transport problem to the set of Gaussian mixture models. As a...