Wasserstein barycenters provide a powerful tool for aggregating probability measures, while leveraging the geometry of their ambient space. Existing discrete methods suffer from poor scalability, as they require access to the complete set of samples from input measures. We address this issue by recasting the original barycenter problem as a gradient flow in the Wasserstein space. Our approach offers two advantages. First, we achieve scalability by sampling mini-batches from the input measures. Second, we incorporate functionals over probability measures, which regularize the barycenter problem through internal, potential, and interaction energies. We present two algorithms for empirical and Gaussian mixture measures, providing convergence guarantees under the Polyak-Łojasiewicz inequality. Experimental validation on toy datasets and domain adaptation benchmarks show that our methods outperform previous discrete and neural net-based methods for computing Wasserstein barycenters.

Hence, incremental DA is a good candidate to enhance the performance of automatic fault diagnosis systems. This paper addresses the challenge of online multi-source In the context of DA, a prominent framework is Optimal domain adaptation (MSDA) in transfer learning, a scenario Transport (OT) [4, 5], which is a mathematical theory where one needs to adapt multiple, heterogeneous source concerned with the displacement of mass at least effort. In domains towards a target domain that comes in a stream. We this paper, we are particularly interested in the Dataset Dictionary introduce a novel approach for the online fit of a Gaussian Learning (DaDiL) framework proposed by [6], especially Mixture Model (GMM), based on the Wasserstein geometry its Gaussian Mixture Model (GMM) formulation [7], of Gaussian measures. We build upon this method and recent which learns to interpolate probability measures in a Wasserstein developments in dataset dictionary learning for proposing a space through dictionary learning.

In this paper we explore domain adaptation through optimal transport. We propose a novel approach, where we model the data distributions through Gaussian mixture models. This strategy allows us to solve continuous optimal transport through an equivalent discrete problem. The optimal transport solution gives us a matching between source and target domain mixture components. From this matching, we can map data points between domains, or transfer the labels from the source domain components towards the target domain. We experiment with 2 domain adaptation benchmarks in fault diagnosis, showing that our methods have state-of-the-art performance.