The MIT Statistics and Data Science Center hosts guest lecturers from around the world in this weekly seminar.
Matrix displacement convexity and intrinsic dimensionality
Abstract: The space of probability measures endowed with the optimal transport metric has a rich structure with applications in probability, analysis, and geometry. The notion of (displacement) convexity in this space was discovered by McCann, and forms the backbone of this theory. I will introduce a new, and stronger, notion of displacement convexity which operates on the matrix level. The motivation behind this definition is to capture the intrinsic dimensionality of probability measures which could have very different behaviors along…