Applied Math Colloquium: Gautam Iyer (Carnegie Mellon University)

Let U be a potential, ε > 0 be a small temperature, and π be a
probability measure with density proportional to e^{-ε U}. How do you
efficiently draw samples from π? This is a challenging question that
arises in many areas ranging from statistical physics to machine
learning. The main difficulty is that the configuration space is so
large that it is computationally infeasible to explore it well enough to
find regions in which π is concentrated, and general algorithms have a
cost that is exponential in dimension, or in 1/ε. This talk will provide
an overview of the area, outlining the main algorithms, a few examples,
and computational challenges. I will conclude by describing recent work
(with D. Slepčev and R. Han) that samples from the Gibbs measure π with
time complexity that is roughly 1/ε^4.