8,526 research outputs found
Fast learning rates for plug-in classifiers under the margin condition
It has been recently shown that, under the margin (or low noise) assumption,
there exist classifiers attaining fast rates of convergence of the excess Bayes
risk, i.e., the rates faster than . The works on this subject
suggested the following two conjectures: (i) the best achievable fast rate is
of the order , and (ii) the plug-in classifiers generally converge
slower than the classifiers based on empirical risk minimization. We show that
both conjectures are not correct. In particular, we construct plug-in
classifiers that can achieve not only the fast, but also the {\it super-fast}
rates, i.e., the rates faster than . We establish minimax lower bounds
showing that the obtained rates cannot be improved.Comment: 36 page
Fast learning rates for plug-in classifiers
It has been recently shown that, under the margin (or low noise) assumption,
there exist classifiers attaining fast rates of convergence of the excess Bayes
risk, that is, rates faster than . The work on this subject has
suggested the following two conjectures: (i) the best achievable fast rate is
of the order , and (ii) the plug-in classifiers generally converge more
slowly than the classifiers based on empirical risk minimization. We show that
both conjectures are not correct. In particular, we construct plug-in
classifiers that can achieve not only fast, but also super-fast rates, that is,
rates faster than . We establish minimax lower bounds showing that the
obtained rates cannot be improved.Comment: Published at http://dx.doi.org/10.1214/009053606000001217 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Permanental fields, loop soups and continuous additive functionals
A permanental field, , is a
particular stochastic process indexed by a space of measures on a set . It
is determined by a kernel , , that need not be symmetric and
is allowed to be infinite on the diagonal. We show that these fields exist when
is a potential density of a transient Markov process in . A
permanental field can be realized as the limit of a renormalized sum of
continuous additive functionals determined by a loop soup of , which we
carefully construct. A Dynkin-type isomorphism theorem is obtained that relates
to continuous additive functionals of (continuous in ),
. Sufficient conditions
are obtained for the continuity of on . The metric
on is given by a proper norm.Comment: Published in at http://dx.doi.org/10.1214/13-AOP893 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The effect of dark strings on semilocal strings
Dark strings have recently been suggested to exist in new models of dark
matter that explain the excessive electronic production in the galaxy. We study
the interaction of these dark strings with semilocal strings which are
solutions of the bosonic sector of the Standard Model in the limit
, where is the Weinberg angle. While
embedded Abelian-Higgs strings exist for generic values of the coupling
constants, we show that semilocal solutions with non-vanishing condensate
inside the string core exist only above a critical value of the Higgs to gauge
boson mass ratio when interacting with dark strings. Above this critical value,
which is greater than unity, the energy per unit length of the semilocal-dark
string solutions is always smaller than that of the embedded Abelian-Higgs-dark
string solutions and we show that Abelian-Higgs-dark strings become unstable
above this critical value. Different from the non-interacting case, we would
thus expect semilocal strings to be stable for values of the Higgs to gauge
boson mass ratio larger than unity. Moreover, the one-parameter family of
solutions present in the non-interacting case ceases to exist when semilocal
strings interact with dark strings.Comment: 16 pages including 6 figures; stability analysis adde
Infinite-horizon choice functions
We analyze infinite-horizon choice functions within the setting of a simple technology. Efficiency and time consistency are characterized by stationary consumption and inheritance functions, as well as a transversality condition. In addition, we consider the equity axioms Suppes-Sen, Pigou-Dalton, and resource monotonicity. We show that Suppes-Sen and Pigou-Dalton imply that the consumption and inheritance functions are monotone with respect to time - thus justifying sustainability - while resource monotonicity implies that the consumption and inheritance functions are monotone with respect to the resource. Examples illustrate the characterization results.Intergenerational resource allocation, infinite-horizon choice
The varying w spread spectrum effect for radio interferometric imaging
We study the impact of the spread spectrum effect in radio interferometry on
the quality of image reconstruction. This spread spectrum effect will be
induced by the wide field-of-view of forthcoming radio interferometric
telescopes. The resulting chirp modulation improves the quality of
reconstructed interferometric images by increasing the incoherence of the
measurement and sparsity dictionaries. We extend previous studies of this
effect to consider the more realistic setting where the chirp modulation varies
for each visibility measurement made by the telescope. In these first
preliminary results, we show that for this setting the quality of
reconstruction improves significantly over the case without chirp modulation
and achieves almost the reconstruction quality of the case of maximal, constant
chirp modulation.Comment: 1 page, 1 figure, Proceedings of the Biomedical and Astronomical
Signal Processing Frontiers (BASP) workshop 201
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