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The Measure of a Model
This paper describes measures for evaluating the three determinants of how
well a probabilistic classifier performs on a given test set. These
determinants are the appropriateness, for the test set, of the results of (1)
feature selection, (2) formulation of the parametric form of the model, and (3)
parameter estimation. These are part of any model formulation procedure, even
if not broken out as separate steps, so the tradeoffs explored in this paper
are relevant to a wide variety of methods. The measures are demonstrated in a
large experiment, in which they are used to analyze the results of roughly 300
classifiers that perform word-sense disambiguation.Comment: 12 pages, uuencoded compressed postscript fil
Isoscaling as a measure of Symmetry Energy in the Lattice Gas Model
The energetic properties of nuclear clusters inside a low-density,
finite-temperature medium are studied with a Lattice Gas Model including
isospin dependence and Coulomb forces. Important deviations are observed
respect to the Fisher approximation of an ideal gas of non-interacting
clusters, but the global energetics can still be approximately expressed in
terms of a simple modified energy-density functional. The multi-fragmentation
regime appears dominated by combinatorial effects in this model, but the
isoscaling of the largest fragment in low energy collisions appears a promising
observable for the experimental measurement of the symmetry energy.Comment: 4 pages, 3 figure, submitted to PR
Statistical properties of the localization measure in a finite-dimensional model of the quantum kicked rotator
We study the quantum kicked rotator in the classically fully chaotic regime
and for various values of the quantum parameter using Izrailev's
-dimensional model for various , which in the limit tends to the exact quantized kicked rotator. By numerically
calculating the eigenfunctions in the basis of the angular momentum we find
that the localization length for fixed parameter values has a
certain distribution, in fact its inverse is Gaussian distributed, in analogy
and in connection with the distribution of finite time Lyapunov exponents of
Hamilton systems. However, unlike the case of the finite time Lyapunov
exponents, this distribution is found to be independent of , and thus
survives the limit . This is different from the tight-binding model
of Anderson localization. The reason is that the finite bandwidth approximation
of the underlying Hamilton dynamical system in the Shepelyansky picture (D.L.
Shepelyansky, {\em Phys. Rev. Lett.} {\bf 56}, 677 (1986)) does not apply
rigorously. This observation explains the strong fluctuations in the scaling
laws of the kicked rotator, such as e.g. the entropy localization measure as a
function of the scaling parameter , where is the
theoretical value of the localization length in the semiclassical
approximation. These results call for a more refined theory of the localization
length in the quantum kicked rotator and in similar Floquet systems, where we
must predict not only the mean value of the inverse of the localization length
but also its (Gaussian) distribution, in particular the variance. In
order to complete our studies we numerically analyze the related behavior of
finite time Lyapunov exponents in the standard map and of the 22
transfer matrix formalism. This paper is extending our recent work.Comment: 12 pages, 9 figures (accepted for publication in Physical Review E).
arXiv admin note: text overlap with arXiv:1301.418
Assessing Financial Model Risk
Model risk has a huge impact on any risk measurement procedure and its
quantification is therefore a crucial step. In this paper, we introduce three
quantitative measures of model risk when choosing a particular reference model
within a given class: the absolute measure of model risk, the relative measure
of model risk and the local measure of model risk. Each of the measures has a
specific purpose and so allows for flexibility. We illustrate the various
notions by studying some relevant examples, so as to emphasize the
practicability and tractability of our approach.Comment: 23 pages, 6 figure
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