Galy-Fajou, ThéoPerrone, ValerioOpper, Manfred2022-01-172022-01-172021-07-30https://depositonce.tu-berlin.de/handle/11303/16139http://dx.doi.org/10.14279/depositonce-14913Variational inference is a powerful framework, used to approximate intractable posteriors through variational distributions. The de facto standard is to rely on Gaussian variational families, which come with numerous advantages: they are easy to sample from, simple to parametrize, and many expectations are known in closed-form or readily computed by quadrature. In this paper, we view the Gaussian variational approximation problem through the lens of gradient flows. We introduce a flexible and efficient algorithm based on a linear flow leading to a particle-based approximation. We prove that, with a sufficient number of particles, our algorithm converges linearly to the exact solution for Gaussian targets, and a low-rank approximation otherwise. In addition to the theoretical analysis, we show, on a set of synthetic and real-world high-dimensional problems, that our algorithm outperforms existing methods with Gaussian targets while performing on a par with non-Gaussian targets.en510 Mathematikvariational inferenceGaussianparticle flowvariable flowArticle1099-4300