Modern data analysis provides scientists with statistical and machine learning algorithmswith impressive performance. In front of their extensive use to tackle problems of constantlygrowing complexity, there is a real need to understand the conditions under which algorithmsare successful or bound to fail. An additional objective is to gain insights...
On s’intéresse dans cette thèse au comportement asymptotique (presque-sûr, en loi, en moyenne) de la variable aléatoire comptant le nombre de zéros de fonctions trigonométriques sur un intervalle donné. On examine en outre si l’on a un phénomène d’universalité, c’est-à-dire si ce nombre dépend ou non de la loi des coefficients, de leur corrélation,...
The thesis is divided into two main parts: i) Nonparametric statistics on high-dimensional and functional spaces, and ii) Nonparametric statistics on Riemannian manifolds. In this part, we will summarize the major contributions of the thesis. Nonparametric statistics on high-dimensional and functional spacesIn statistical learning, we introduce a n...
Alzheimer's disease (AD) is a neurodegenerative disorder characterized by biological and morphological processes which spread over decades, ultimately leading to cognitive and behavioral decline. These processes can be monitored thanks to biomarkers and imaging measurements. As the mechanisms underlying the evolution of the pathology remain partial...
Collective motions describe populations in which individuals' interactions are the driving force behind their displacements and their transformation over time. Understanding and controlling collective motions are significant issues in many fields, especially for the study of ecosystems (swarm dynamics), safety in large gatherings and buildings (cro...
Les changements climatiques entraînent régulièrement des phénomènes menaçant directement l'environnement et l'humanité. Dans ce contexte, la météorologie joue de plus en plus un rôle important dans la compréhension et la prévision de ces phénomènes. Le problème de fiabilisation des observations est essentiel pour le raisonnement numérique et la qua...
Gaussian Processes (GPs) are an attractive specific way of doing non-parametric Bayesian modeling in a supervised learning problem. It is well-known that GPs are able to make inferences as well as predictive uncertainties with a firm mathematical background. However, GPs are often unfavorable by the practitioners due to their kernel's expressivenes...
In this thesis, we explore the possibility of virtual coronary stenosis assessment, through thesimulation of Fractional Flow Reserve (FFR) measurement, that is an indispensable but bindingtool during diagnosis. First, we use a 2D non Newtonian flow model, and later a weaklycoupled FSI model to make a preliminary study of the main features of flow o...
In this thesis, we explore the possibility of virtual coronary stenosis assessment, through the simulation of Fractional Flow Reserve (FFR) measurement, that is an indispensable but binding tool during diagnosis. First, we use a 2D non Newtonian flow model, and later a weakly coupled FSI model to make a preliminary study of the main features of flo...
This thesis focuses on the simultaneous optimization of expensive-to-evaluate functions that depend on a high number of parameters. This situation is frequently encountered in fields such as design engineering through numerical simulation. Bayesian optimization relying on surrogate models (Gaussian Processes) is particularly adapted to this context...
