3,858 research outputs found
Nonasymptotic analysis of adaptive and annealed Feynman-Kac particle models
Sequential and quantum Monte Carlo methods, as well as genetic type search
algorithms can be interpreted as a mean field and interacting particle
approximations of Feynman-Kac models in distribution spaces. The performance of
these population Monte Carlo algorithms is strongly related to the stability
properties of nonlinear Feynman-Kac semigroups. In this paper, we analyze these
models in terms of Dobrushin ergodic coefficients of the reference Markov
transitions and the oscillations of the potential functions. Sufficient
conditions for uniform concentration inequalities w.r.t. time are expressed
explicitly in terms of these two quantities. We provide an original
perturbation analysis that applies to annealed and adaptive Feynman-Kac models,
yielding what seems to be the first results of this kind for these types of
models. Special attention is devoted to the particular case of Boltzmann-Gibbs
measures' sampling. In this context, we design an explicit way of tuning the
number of Markov chain Monte Carlo iterations with temperature schedule. We
also design an alternative interacting particle method based on an adaptive
strategy to define the temperature increments. The theoretical analysis of the
performance of this adaptive model is much more involved as both the potential
functions and the reference Markov transitions now depend on the random
evolution on the particle model. The nonasymptotic analysis of these complex
adaptive models is an open research problem. We initiate this study with the
concentration analysis of a simplified adaptive models based on reference
Markov transitions that coincide with the limiting quantities, as the number of
particles tends to infinity.Comment: Published at http://dx.doi.org/10.3150/14-BEJ680 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Stationary probability density of stochastic search processes in global optimization
A method for the construction of approximate analytical expressions for the
stationary marginal densities of general stochastic search processes is
proposed. By the marginal densities, regions of the search space that with high
probability contain the global optima can be readily defined. The density
estimation procedure involves a controlled number of linear operations, with a
computational cost per iteration that grows linearly with problem size
Hypocoercivity in metastable settings and kinetic simulated annealing
Combining classical arguments for the analysis of the simulated annealing
algorithm with the more recent hypocoercive method of distorted entropy, we
prove the convergence for large time of the kinetic Langevin annealing with
logarithmic cooling schedule
Modelling and estimation for random fields
Caption title.Includes bibliographical references (p. [21]-[22]).Supported by Air Force Office of Scientific Research. AFOSR-89-0276-C Supported by the Army Research Office. DAAL03-92-G-0115Sanjoy K. Mitter
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