# Nawaf Bou-Rabee: Upper Bounds for Mixing Time of Unadjusted Hamiltonian Monte Carlo by Couplings

**Time: **
Mon 2021-12-06 15.15 - 16.15

**Location: **
KTH, Room 3721, Lindstedtsvägen 25 (also Zoom meeting ID: 621 4469 8204)

**Lecturer: **
Nawaf Bou-Rabee (Rutgers)

### Abstract

Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo method that is frequently used in statistical physics, statistics, and machine learning. The transition step of HMC uses a combination of Hamiltonian dynamics and velocity randomizations. The Hamiltonian dynamics is typically discretized using a reversible/volume-preserving integrator, and the discretization bias can either be borne (unadjusted HMC) or eliminated by Metropolis-Hastings (adjusted HMC). Despite its empirical success, until a few years ago there were few mixing time guarantees for HMC. Now, approaches to quantify convergence to equilibrium based on coupling, conductance and hypocoercivity have been developed. I will talk about the coupling approach, and show how it can be used to obtain mixing time guarantees for unadjusted HMC in some high-dimensional and non-convex models. This talk is based on joint work with Andreas Eberle (Bonn) and Katharina Schuh (Bonn).