Computational Mathematics & Statistics Seminar by Yiwei Wang: Energetic Variational Inference

Speaker:

Yiwei Wang, Postdoc, Department of Applied Mathematics, Illinois Institute of Technology

Title:

Energetic Variational Inference 

Abstract:

In this talk, we present a variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing flow-based Variational Inference methods, including the popular Stein Variational Gradient Descent (SVGD) approach. More importantly, many new VI schemes can be created under this framework. As an illustration, we propose a new particle-based EVI (ParVI) scheme, which performs the particle-based approximation of the density first and then uses the approximated density in the variational procedure. Thanks to this order of approximation and variation, we can construct a numerical algorithm based on a minimizing movement scheme (implicit Euler scheme). Numerical experiments show the proposed method outperforms some existing ParVI methods in terms of fidelity to the target distribution. This is a joint work with Prof. Chun Liu and Prof. Lulu Kang.

 

Computational Mathematics & Statistics