Algorithms and structure on the space of probability measures

• Applicant: Professor Dr. Stephan Eckstein
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 553088969

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.

• DFG Programme: Independent Junior Research Groups