Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g., decision making, image processing, machine learning for both classification, and regression. Tools for measure identificati...
Electromagnetic (EM) Inverse Problems have a long history of important medical, industrial and geophysical applications. The underlying theoretical and computational challenges have stimulated scientific research for more than a century and significant advances have been witnessed in this field regarding experimental capabilities, broadening fields...
Motivated by recent developments in the fields of large deviations for interacting particle systems and mean field control, we establish a comparison principle for the Hamilton–Jacobi equation corresponding to linearly controlled gradient flows of an energy function E defined on a metric space (E,d). Our analysis is based on a systematic use of the...
Optimal transport theory not only defines a distance between probability measures but also provides a geometric way to transport a set of points to another according to the principle of least effort. This dual aspect has left the door wide open for applications in domain adaptation, a subfield of statistical learning theory that takes into account ...
Accounting for climate transition risks is one of the most important challenges in the transition to a low-carbon economy. Banks are encouraged to align their investment portfolios to CO2 trajectories fixed by international agreements, showing the necessity of a quantitative methodology to implement it. We propose a mathematical formulation for thi...
Augmentations and other transformations of data, either in the input or latent space, are a critical component of modern machine learning systems. While these techniques are widely used in practice and known to provide improved generalization in many cases, it is still unclear how data manipulation impacts learning and generalization. To take a ste...
Cette thèse étudie des problèmes variationnels comprenant plusieurs fonctionnelles de transport optimal. Un exemple populaire est le barycentre Wasserstein qui peut être vu en tant que moyenne dans l'espace de Wasserstein d'ordre 2. Depuis son introduction en 2011 de Agueh et Carlier, il est devenu très populaire en statistiques, machine learning e...
In this work, we study the structure of minimizers of the quadratic Gromov--Wasserstein (GW) problem on Euclidean spaces for two different costs. The first one is the scalar product for which we prove that it is always possible to find optimizers as Monge maps and we detail the structure of such optimal maps. The second cost is the squared Euclidea...
Elementary Hodge decompositions break down any vector field into a sum of a gradient field and a divergence-free vector field. Such a result is extended to finite irreducible and reversible Markov processes, where vector fields correspond to anti-symmetric functions on the oriented edges of the underlying graph.
Published in Medical image analysis
Brain pathologies often manifest as partial or complete loss of tissue. The goal of many neuroimaging studies is to capture the location and amount of tissue changes with respect to a clinical variable of interest, such as disease progression. Morphometric analysis approaches capture local differences in the distribution of tissue or other quantiti...
