Manifold Gaussian Variational Bayes on the Precision Matrix

arXiv:2210.14598v4 Announce Type: replace-cross
Abstract: We propose an optimization algorithm for Variational Inference (VI) in complex models. Our approach relies on natural gradient updates where the variational space is a Riemann manifold. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Our Manifold Gaussian Variational Bayes on the Precision matrix (MGVBP) solution provides simple update rules, is straightforward to implement, and the use of the precision matrix parametrization …

abstract algorithm arxiv bayes covariance cs.lg gradient inference manifold matrix natural optimization positive precision space stat.ml type updates