Recorded 19 May 2025. Jean Lasserre of Université de Toulouse III (Paul Sabatier) LAAS-CNRS presents "Gaussian mixtures closest to a given measure via optimal transport" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Abstract: Given a determinate (multivariate) probability measure « \mu », we characterize Gaussian mixtures « \nu_\phi » which minimize the Wasserstein distance « W_2(\mu,\nu_\phi) » to « \mu » when the mixing probability measure « \phi » on the parameters « \m,\bSigma » of the Gaussians is supported on a given compact semi-algebraic set « S ». Such mixtures are optimal solutions of a particular optimal transport (OT) problem where the marginal « \nu_{\phi} » of the OT problem is also unknown via the mixing measure variable « \phi ». Next by using a well-known specific property of Gaussian measures, this optimal transport is then viewed as a Generalized Moment Problem (GMP) for which we provide a ``mesh-free" numerical scheme. In particular, we do not assume that the mixing measure is finitely supported nor that the variance is the same for all components. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-and-numerical-methods-for-non-commutative-optimal-transport/