Talk page

Title:
Convergence of Hamiltonian Monte Carlo and Faster Polytope Volume Computation

Speaker:
Yin Tat Lee

Abstract:
We explain the Hamiltonian Monte Carlo method and apply it to the problem of 1) generating uniform random points from polytopes, 2) computing the volume of polytopes. For polytopes in R^n specified by O(n) inequalities, the resulting algorithm for both problems takes merely O*(n^1.667) steps. For volume computation, this is a huge improvement over the previous best algorithm that requires O(n^4) steps. The key idea is to prove certain isoperimetric inequalities on manifolds defined by log barrier functions. Joint work with Santosh Vempala

Link:
https://www.msri.org/workshops/811/schedules/23260

Workshop:
MSRI- Geometric functional analysis and applications