A Geometric Variational Approach to Bayesian Inference
贝叶斯推断的几何变分方法
We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher–Rao metric on the manifold of probability density functions. Under the square-root density representation, the manifold can be identified with the positive orthant of the unit hypersphere S∞ in L2, and the Fisher–Rao metric reduces to the standard L2 metric. Exploiting such a Riemannian structure, we formulate the task of approximating the…