Elsa Cazelles – Winner of the ANR Young Researchers Program
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Elsa Cazelles, a member of the PDE-AI project at the Toulouse Institute for Computer Science Research, has been selected for the ANR’s Young Researchers Program with the ENTENTE project.
The ENTENTE project aims to develop machine learning methods tailored to data modeled by probability distributions (e.g., images, word distributions, individual cells, point clouds, etc.). When equipped with the Wasserstein distance, the set of probability distributions defines a positively curved space, which is incompatible with classical learning algorithms. The project will explore embeddings of measures into latent spaces (e.g., Hilbert spaces, Gaussian mixtures) that preserve the underlying geometry of the data, whether induced by the Wasserstein distance or by alpha-connections from information theory. These embeddings and learning methods will be compared in terms of stability, statistical guarantees, and algorithmic efficiency.
This project aims to further the objectives of the PDE-AI project by addressing, on the one hand, problems in statistical learning based on data in the form of probability measures, and, on the other hand, challenges related to sampling and data generation (e.g., for unsupervised learning) by drawing on the geometry of alpha-flots. ENTENTE will draw in particular on the expertise of Alice Le Brigant and Clément Bonet, affiliated with the Toulouse and Institut Polytechnique de Paris hubs of the PDE-AI project, respectively, and will welcome a new collaborator, Felipe Tobar, from Imperial College London. It will also provide funding for three Master’s 2 internships, one doctoral fellowship, and one 18-month postdoctoral fellows
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