24,689 research outputs found
Orthogonal parallel MCMC methods for sampling and optimization
Monte Carlo (MC) methods are widely used for Bayesian inference and
optimization in statistics, signal processing and machine learning. A
well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms.
In order to foster better exploration of the state space, specially in
high-dimensional applications, several schemes employing multiple parallel MCMC
chains have been recently introduced. In this work, we describe a novel
parallel interacting MCMC scheme, called {\it orthogonal MCMC} (O-MCMC), where
a set of "vertical" parallel MCMC chains share information using some
"horizontal" MCMC techniques working on the entire population of current
states. More specifically, the vertical chains are led by random-walk
proposals, whereas the horizontal MCMC techniques employ independent proposals,
thus allowing an efficient combination of global exploration and local
approximation. The interaction is contained in these horizontal iterations.
Within the analysis of different implementations of O-MCMC, novel schemes in
order to reduce the overall computational cost of parallel multiple try
Metropolis (MTM) chains are also presented. Furthermore, a modified version of
O-MCMC for optimization is provided by considering parallel simulated annealing
(SA) algorithms. Numerical results show the advantages of the proposed sampling
scheme in terms of efficiency in the estimation, as well as robustness in terms
of independence with respect to initial values and the choice of the
parameters
Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima
The optimization of three problems with high dimensionality and many local minima are investigated
under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO
package, and QNSTOP, a new algorithm developed at Indiana University
Population annealing: Theory and application in spin glasses
Population annealing is an efficient sequential Monte Carlo algorithm for
simulating equilibrium states of systems with rough free energy landscapes. The
theory of population annealing is presented, and systematic and statistical
errors are discussed. The behavior of the algorithm is studied in the context
of large-scale simulations of the three-dimensional Ising spin glass and the
performance of the algorithm is compared to parallel tempering. It is found
that the two algorithms are similar in efficiency though with different
strengths and weaknesses.Comment: 16 pages, 10 figures, 4 table
Equilibrium Sampling From Nonequilibrium Dynamics
We present some applications of an Interacting Particle System (IPS)
methodology to the field of Molecular Dynamics. This IPS method allows several
simulations of a switched random process to keep closer to equilibrium at each
time, thanks to a selection mechanism based on the relative virtual work
induced on the system. It is therefore an efficient improvement of usual
non-equilibrium simulations, which can be used to compute canonical averages,
free energy differences, and typical transitions paths
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