Local Step Size Adaptation for Hamiltonian MCMC

• Activity Number: 278
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew Douglas Hoffman*+
• Companies: Adobe Research
• Keywords: Markov chain Monte Carlo ; Hamiltonian Monte Carlo ; No-U-Turn Sampler ; Computation ; Riemannian Manifold HMC

Abstract

Hamiltonian/hybrid Monte Carlo (HMC) is a Markov chain Monte Carlo algorithm that can generate samples from Bayesian posterior distributions much more quickly than methods such as Gibbs sampling or random-walk Metropolis. HMC's efficiency depends strongly on the ability of the user to specify (at a minimum) a step size parameter; different applications demand different step sizes, and different step sizes may be optimal in different regions of the posterior. In this paper, we develop proxy-eigenvalue adaptation (PEA), which adjusts HMC's step size based on the local curvature of the posterior. Unlike HMC, our method is able to sample efficiently from heavy- and light-tailed distributions. Our method is based on Riemannian manifold HMC, but is applicable to models with priors that are not jointly log-concave, exhibits linear (rather than cubic) scaling with dimensionality, requires only the gradient of the log-posterior (rather than the three-way array of third derivatives), and uses a fully explicit numerical integration scheme. PEA can be combined with the recently introduced no-U-turn sampler (NUTS) to yield PEANUTS, which locally adapts both step sizes and trajectory lengths.