4,557 research outputs found
Population Annealing with Weighted Averages: A Monte Carlo Method for Rough Free Energy Landscapes
The population annealing algorithm introduced by Hukushima and Iba is
described. Population annealing combines simulated annealing and Boltzmann
weighted differential reproduction within a population of replicas to sample
equilibrium states. Population annealing gives direct access to the free
energy. It is shown that unbiased measurements of observables can be obtained
by weighted averages over many runs with weight factors related to the free
energy estimate from the run. Population annealing is well suited to
parallelization and may be a useful alternative to parallel tempering for
systems with rough free energy landscapes such as spin glasses. The method is
demonstrated for spin glasses.Comment: 9 pages, 5 figures; version 2 has improved figure 5 and new titl
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
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