Stochastic & Multiscale Modeling and Computation Seminar by Yiwei Wang: Energetic Variational Inference: A Variational Approach to Bayesian Statistics and Beyond
Speaker:
Yiwei Wang, Dept. of Applied Mathematics, Illinois Institute
of Technology
Title:
Energetic variational inference: a variational approach to
Bayesian statistics and beyond
Abstract:
Bayesian inference is one of the most important techniques
in modern statistics and data science. In this talk, we present a
variational framework to Bayesian methods, called energetic
variational inference (EVI), which views a posterior as a minimizer of
a functional and uses an energy-dissipation law to characterize the
minimization procedure. The framework is motivated by non-equilibrium
physics. Using the EVI framework, we can derive many existing
flow-based Variational Inference (VI) methods, including the popular
Stein Variational Gradient Descent (SVGD) approach. More importantly,
many new algorithms can be created under this framework. As an
example, we propose a new particle-based VI (ParVI) scheme, which
performs the particle-based approximation of the density first and
then uses the approximated density in the variational procedure. The
“approximation-then-variation” procedure enables us to 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. The framework can be applied to a wide class of
unsupervised learning problems beyond the Bayesian methods, such as
the generative model and the density estimation. This is joint work
with Prof. Chun Liu and Prof. Lulu Kang.
Note: Face coverings will be required. Even if you are fully vaccinated, all students, staff, faculty, and guests must wear a face covering indoors. The university will review and revise the mask protocol as appropriate given changes to state and city public-health guidelines.
Stochastic & Multiscale Modeling and Computation