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The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method

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posted on 2018-06-06, 22:31 authored by Alexandre Bouchard-Côté, Sebastian J. Vollmer, Arnaud Doucet

Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis–Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature (Peters and de With 2012) where the target distribution is explored using a continuous-time nonreversible piecewise-deterministic Markov process. In the Metropolis–Hastings algorithm, a trial move to a region of lower target density, equivalently of higher “energy,” than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. By reformulating this algorithm using inhomogeneous Poisson processes, we exploit standard sampling techniques to simulate exactly this Markov process in a wide range of scenarios of interest. Additionally, when the target distribution is given by a product of factors dependent only on subsets of the state variables, such as the posterior distribution associated with a probabilistic graphical model, this method can be modified to take advantage of this structure by allowing computationally cheaper “local” bounces, which only involve the state variables associated with a factor, while the other state variables keep on evolving. In this context, by leveraging techniques from chemical kinetics, we propose several computationally efficient implementations. Experimentally, this new class of Markov chain Monte Carlo schemes compares favorably to state-of-the-art methods on various Bayesian inference tasks, including for high-dimensional models and large datasets. Supplementary materials for this article are available online.

Funding

Alexandre Bouchard-Côté’s research is partially supported by a Discovery Grant from the National Science and Engineering Research Council. Arnaud Doucet’s research is partially supported by the Engineering and Physical Sciences Research Council (EPSRC), Grants EP/K000276/1, EP/K009850/1 and by the Air Force Office of Scientific Research/Asian Office of Aerospace Research and Development, Grant AFOSRA/AOARD-144042. Sebastian Vollmer’s research is partially supported by the EPSRC Grants EP/K009850/1 and EP/N000188/1.

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