341,047 research outputs found
Critical Slowing-Down in Landau Gauge-Fixing Algorithms
We study the problem of critical slowing-down for gauge-fixing algorithms
(Landau gauge) in lattice gauge theory on a -dimensional lattice. We
consider five such algorithms, and lattice sizes ranging from to
(up to in the case of Fourier acceleration). We measure four
different observables and we find that for each given algorithm they all have
the same relaxation time within error bars. We obtain that: the so-called {\em
Los Alamos} method has dynamic critical exponent , the {\em
overrelaxation} method and the {\em stochastic overrelaxation} method have , the so-called {\em Cornell} method has slightly smaller than
and the {\em Fourier acceleration} method completely eliminates critical
slowing-down. A detailed discussion and analysis of the tuning of these
algorithms is also presented.Comment: 40 pages (including 10 figures). A few modifications, incorporating
referee's suggestions, without the length reduction required for publicatio
Learning Active Basis Models by EM-Type Algorithms
EM algorithm is a convenient tool for maximum likelihood model fitting when
the data are incomplete or when there are latent variables or hidden states. In
this review article we explain that EM algorithm is a natural computational
scheme for learning image templates of object categories where the learning is
not fully supervised. We represent an image template by an active basis model,
which is a linear composition of a selected set of localized, elongated and
oriented wavelet elements that are allowed to slightly perturb their locations
and orientations to account for the deformations of object shapes. The model
can be easily learned when the objects in the training images are of the same
pose, and appear at the same location and scale. This is often called
supervised learning. In the situation where the objects may appear at different
unknown locations, orientations and scales in the training images, we have to
incorporate the unknown locations, orientations and scales as latent variables
into the image generation process, and learn the template by EM-type
algorithms. The E-step imputes the unknown locations, orientations and scales
based on the currently learned template. This step can be considered
self-supervision, which involves using the current template to recognize the
objects in the training images. The M-step then relearns the template based on
the imputed locations, orientations and scales, and this is essentially the
same as supervised learning. So the EM learning process iterates between
recognition and supervised learning. We illustrate this scheme by several
experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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