Algorithms and structure on the space of probability measures

01/02/2025 to 31/01/2028

This project aims to advance computational methods within the space
of probability measures with a particular focus on its widespread use
in machine learning. Our first objective is to deepen the mathematical
understanding of algorithmic procedures on this space, such as ones
to compute optimal transport distances or gradient flows. The second
objective is to introduce flexible tools tailored for integrating real-world
structural knowledge into the space of probability measures. This is
particularly relevant in, and motivated by, the fields of causal
inference and graph neural networks. The two objectives are
inherently interconnected: developing new tools not only inspires
novel algorithmic strategies but also, as our understanding of these
algorithms deepens, this in turn motivates the creation of new tools,
thereby further enriching the computational landscape within the
space of probability measures.