Transport optimal pour l’apprentissage par transfert entre les espaces

Abstract: In the recent years, the remarkable versatility of optimal transport theory has gone far beyond the classic comparison of the probability measures living in the same underlying space. In this thesis, we are interested in the optimal transport problems between incomparable spaces. More precisely, we focus on the marginal relaxation of the (balanced) Gromov-Wasserstein and Co-Optimal Transport, as well as the integration of prior knownledge into Gromov-Wasserstein distance and its unbalanced formulation. We start with the Co-Optimal Transport in continuous setting, which serves as the first step towards the study of the entropic approximation and unbalanced extension.
Then, we introduce the unbalanced formulation of the Co-Optimal Transport and show its robustness to outliers, by contrast to the balanced counterpart. Next, we propose to use the fused unbalanced Gromov-Wasserstein divergence to align the cortical surfaces, by simultaneously exploiting the functional signals and anatomical structure of human brain. Finally, we further empower the Gromov-Wasserstein distance with the ability to manipulate more efficiently the input data and to perform meaningful genomic feature matching.

Keywords: Unbalanced Optimal Transport, Gromov-Wasserstein, Co-Optimal Transport, Heterogeneous Domain Adaptation