Gaussian Mixtures Closest to a Given Measure via Optimal Transport

In this 43-minute lecture, Jean Lasserre from Université de Toulouse III (Paul Sabatier) LAAS-CNRS explores the characterization of Gaussian mixtures that minimize the Wasserstein distance to a given probability measure through optimal transport methods. Recorded at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop on May 19, 2025, discover how to determine optimal Gaussian mixtures when the mixing probability measure is supported on a compact semi-algebraic set. Learn how this optimal transport problem can be viewed as a Generalized Moment Problem (GMP) and understand the "mesh-free" numerical scheme for solving it without assuming finite support for the mixing measure or uniform variance across components. The presentation provides mathematical insights for researchers working in optimal transport, statistical modeling, and computational mathematics.