Hamiltonian Monte Carlo with Reduced Momentum Flips

Abstract

Hamiltonian Monte Carlo (or hybrid Monte Carlo) with partial momentum refreshment explores the state space more slowly than it otherwise would due to the momentum reversals which occur on proposal rejection. These cause trajectories to double back on themselves, leading to random walk behavior on timescales longer than the typical rejection time, and leading to slower mixing. I present a technique by which the number of momentum reversals can be reduced. This is accomplished by maintaining the net exchange of probability between states with opposite momenta, but reducing the rate of exchange in both directions such that it is 0 in one direction. An experiment illustrates these reduced momentum flips accelerating mixing for a particular distribution.