Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry

The videos illustrate the computation of consensus-based optimization (CBO) algorithm for Gaussian Variational Inference problems. Each particle is a Gaussian probability measure which interacts with the others via a stochastic consensus dynamics. The evolution is defined in the linearized Bures-Wasserstein space.In the video, the contour lines describe the target measure we aim to approximate. Four different target measures are considered. The 20 particles (in red) aim to find the Gaussian measure which minimizes the KL divergence with respect to the target. For comparison with state of the art methods, we also include four videos illustrating the evolution of a (Bures-Wasserstein) Gradient Flow algorithm.