Hamiltonian Monte Carlo with Reduced Momentum Flips
This work addresses a specific inefficiency in Hamiltonian Monte Carlo methods, which is incremental for practitioners in computational statistics and machine learning.
The paper tackles the problem of slow state space exploration in Hamiltonian Monte Carlo due to momentum reversals on proposal rejection, which cause random walk behavior and slower mixing. The authors present a technique to reduce the number of momentum reversals, and an experiment shows it accelerates mixing for a specific distribution.
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.