2,502 research outputs found
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
Non-negative mixtures
This is the author's accepted pre-print of the article, first published as M. D. Plumbley, A. Cichocki and R. Bro. Non-negative mixtures. In P. Comon and C. Jutten (Ed), Handbook of Blind Source Separation: Independent Component Analysis and Applications. Chapter 13, pp. 515-547. Academic Press, Feb 2010. ISBN 978-0-12-374726-6 DOI: 10.1016/B978-0-12-374726-6.00018-7file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:p\PlumbleyCichockiBro10-non-negative.pdf:PDF owner: markp timestamp: 2011.04.2
Spherical Hamiltonian Monte Carlo for Constrained Target Distributions
We propose a new Markov Chain Monte Carlo (MCMC) method for constrained
target distributions. Our method first maps the -dimensional constrained
domain of parameters to the unit ball . Then, it augments the
resulting parameter space to the -dimensional sphere, . The
boundary of corresponds to the equator of . This
change of domains enables us to implicitly handle the original constraints
because while the sampler moves freely on the sphere, it proposes states that
are within the constraints imposed on the original parameter space. To improve
the computational efficiency of our algorithm, we split the Lagrangian dynamics
into several parts such that a part of the dynamics can be handled analytically
by finding the geodesic flow on the sphere. We apply our method to several
examples including truncated Gaussian, Bayesian Lasso, Bayesian bridge
regression, and a copula model for identifying synchrony among multiple
neurons. Our results show that the proposed method can provide a natural and
efficient framework for handling several types of constraints on target
distributions
Automatic surrogate model type selection during the optimization of expensive black-box problems
The use of Surrogate Based Optimization (SBO) has become commonplace for optimizing expensive black-box simulation codes. A popular SBO method is the Efficient Global Optimization (EGO) approach. However, the performance of SBO methods critically depends on the quality of the guiding surrogate. In EGO the surrogate type is usually fixed to Kriging even though this may not be optimal for all problems. In this paper the authors propose to extend the well-known EGO method with an automatic surrogate model type selection framework that is able to dynamically select the best model type (including hybrid ensembles) depending on the data available so far. Hence, the expected improvement criterion will always be based on the best approximation available at each step of the optimization process. The approach is demonstrated on a structural optimization problem, i.e., reducing the stress on a truss-like structure. Results show that the proposed algorithm consequently finds better optimums than traditional kriging-based infill optimization
Tunneling behavior of Ising and Potts models in the low-temperature regime
We consider the ferromagnetic -state Potts model with zero external field
in a finite volume and assume that the stochastic evolution of this system is
described by a Glauber-type dynamics parametrized by the inverse temperature
. Our analysis concerns the low-temperature regime ,
in which this multi-spin system has stable equilibria, corresponding to the
configurations where all spins are equal. Focusing on grid graphs with various
boundary conditions, we study the tunneling phenomena of the -state Potts
model. More specifically, we describe the asymptotic behavior of the first
hitting times between stable equilibria as in probability,
in expectation, and in distribution and obtain tight bounds on the mixing time
as side-result. In the special case , our results characterize the
tunneling behavior of the Ising model on grid graphs.Comment: 13 figure
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