7,414 research outputs found
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
Faster Convex Optimization: Simulated Annealing with an Efficient Universal Barrier
This paper explores a surprising equivalence between two seemingly-distinct
convex optimization methods. We show that simulated annealing, a well-studied
random walk algorithms, is directly equivalent, in a certain sense, to the
central path interior point algorithm for the the entropic universal barrier
function. This connection exhibits several benefits. First, we are able improve
the state of the art time complexity for convex optimization under the
membership oracle model. We improve the analysis of the randomized algorithm of
Kalai and Vempala by utilizing tools developed by Nesterov and Nemirovskii that
underly the central path following interior point algorithm. We are able to
tighten the temperature schedule for simulated annealing which gives an
improved running time, reducing by square root of the dimension in certain
instances. Second, we get an efficient randomized interior point method with an
efficiently computable universal barrier for any convex set described by a
membership oracle. Previously, efficiently computable barriers were known only
for particular convex sets
A Bayesian approach to discrete object detection in astronomical datasets
A Bayesian approach is presented for detecting and characterising the signal
from discrete objects embedded in a diffuse background. The approach centres
around the evaluation of the posterior distribution for the parameters of the
discrete objects, given the observed data, and defines the
theoretically-optimal procedure for parametrised object detection. Two
alternative strategies are investigated: the simultaneous detection of all the
discrete objects in the dataset, and the iterative detection of objects. In
both cases, the parameter space characterising the object(s) is explored using
Markov-Chain Monte-Carlo sampling. For the iterative detection of objects,
another approach is to locate the global maximum of the posterior at each
iteration using a simulated annealing downhill simplex algorithm. The
techniques are applied to a two-dimensional toy problem consisting of Gaussian
objects embedded in uncorrelated pixel noise. A cosmological illustration of
the iterative approach is also presented, in which the thermal and kinetic
Sunyaev-Zel'dovich effects from clusters of galaxies are detected in microwave
maps dominated by emission from primordial cosmic microwave background
anisotropies.Comment: 20 pages, 12 figures, accepted by MNRAS; contains some additional
material in response to referee's comment
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