1,211 research outputs found
Active classification with comparison queries
We study an extension of active learning in which the learning algorithm may
ask the annotator to compare the distances of two examples from the boundary of
their label-class. For example, in a recommendation system application (say for
restaurants), the annotator may be asked whether she liked or disliked a
specific restaurant (a label query); or which one of two restaurants did she
like more (a comparison query).
We focus on the class of half spaces, and show that under natural
assumptions, such as large margin or bounded bit-description of the input
examples, it is possible to reveal all the labels of a sample of size using
approximately queries. This implies an exponential improvement over
classical active learning, where only label queries are allowed. We complement
these results by showing that if any of these assumptions is removed then, in
the worst case, queries are required.
Our results follow from a new general framework of active learning with
additional queries. We identify a combinatorial dimension, called the
\emph{inference dimension}, that captures the query complexity when each
additional query is determined by examples (such as comparison queries,
each of which is determined by the two compared examples). Our results for half
spaces follow by bounding the inference dimension in the cases discussed above.Comment: 23 pages (not including references), 1 figure. The new version
contains a minor fix in the proof of Lemma 4.
The absolute position of a resonance peak
It is common practice in scattering theory to correlate between the position
of a resonance peak in the cross section and the real part of a complex energy
of a pole of the scattering amplitude. In this work we show that the resonance
peak position appears at the absolute value of the pole's complex energy rather
than its real part. We further demonstrate that a local theory of resonances
can still be used even in cases previously thought impossible
First principles derivation of a Rayleigh Gans Debye model for scattering from anisotropic inhomogeneities
Scattering problems are important in describing light propagation in wide
ranging media such as the atmosphere, colloidal solutions, metamaterials, glass
ceramic composites, transparent polycrystalline ceramics, and surfaces. The
Rayleigh Gans Debye (RGD) approximation has enjoyed great success in describing
a wide range of scattering phenomena. We derive a generalized RGD formulation
from the perturbation of Maxwell equations. In contrast to most treatments of
RGD scattering, our formulation can model any soft scattering phenomena in
linear media, including scattering by stochastic process, lossy media, and by
anisotropic inhomogeneities occurring at multiple length scales. Our
first-principles derivation makes explicit underlying assumptions and provides
jumping off points for more general treatments. The derivation also facilitates
a deeper understanding of soft scattering. It is demonstrated that sources of
scattering are not interfaces as is often presumed, but excess accelerating
charges emitting uncompensated radiation. Approximations to the equations are
also presented and discussed. For example, the scattering coefficient in the
large size RGD limit is shown to be proportional to the correlation length and
the variance of a projected phase shift
Chromatic Cyclotomic Extensions
We construct Galois extensions of the T(n)-local sphere, lifting all finite
abelian Galois extensions of the K(n)-local sphere. This is achieved by
realizing them as higher semiadditive analogues of cyclotomic extensions.
Combining this with a general form of Kummer theory, we lift certain elements
from the K(n)-local Picard group to the T(n)-local Picard group.Comment: 48 pages. Comments are welcome
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