In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the last two discharge times, and possibly more. Such multi-time processes arise in many other areas and there is no universal limitation on the number of times to be used. T...
A key challenge in Machine Learning (ML) is to design models able to learn efficiently from graphs, characterized by nodes with attributes and a prescribed structure encoding their relationships. Graph Representation Learning (GRL) aims to encode these two sources of heterogeneity into a vectorial graph embedding easing downstream tasks. In this fi...
Mixture models are relevant to represent several sub-populations inside a global population. In these models, the weights parameter accounts for the proportions of the different sub-populations that compose the global population. In this thesis, we develop new tools for the estimation of the weights parameter. Our developments are based on the noti...
This paper focuses on a new approach to describe coastal morphodynamics, based on optimization theory, and more specifically on the assumption that a sandy seabed evolves in order to minimize a wave-related function, the choice of which depends on what is considered the driving force behind coastal morphodynamics. The numerical model derived from t...
Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples. In such situations, the goal is to find a transport map that has good generalization properties on unseen data, ideally the closest map to the ground truth, unknown in pr...
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [10] for mixtures of gaussian measures to other mixtures. We first prove in a general setting that for a set of at...
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...
In the context of intellectual property in the manufacturing industry, know-how is referred to practical knowledge on how to accomplish a specific task. This know-how is often difficult to be synthesised in a set of rules or steps as it remains in the intuition and expertise of engineers, designers, and other professionals. Today, a new research li...
Inom reglerteknik har integrationen av maskininlärningsmetoder framträtt som en central strategi för att förbättra prestanda och adaptivitet hos styrsystem. Betydande framsteg har gjorts inom flera viktiga aspekter av reglerkretsen, såsom inlärningsbaserade metoder för systemidentifiering och parameterskattning, filtrering och brusreducering samt r...
We show that the derivatives of the Sinkhorn–Knopp algorithm, or iterative proportional fitting procedure, converge towards the derivatives of the entropic regularization of the optimal transport problem with a locally uniform linear convergence rate.
