2,354 research outputs found
Elastic-Net Regularization in Learning Theory
Within the framework of statistical learning theory we analyze in detail the
so-called elastic-net regularization scheme proposed by Zou and Hastie for the
selection of groups of correlated variables. To investigate on the statistical
properties of this scheme and in particular on its consistency properties, we
set up a suitable mathematical framework. Our setting is random-design
regression where we allow the response variable to be vector-valued and we
consider prediction functions which are linear combination of elements ({\em
features}) in an infinite-dimensional dictionary. Under the assumption that the
regression function admits a sparse representation on the dictionary, we prove
that there exists a particular ``{\em elastic-net representation}'' of the
regression function such that, if the number of data increases, the elastic-net
estimator is consistent not only for prediction but also for variable/feature
selection. Our results include finite-sample bounds and an adaptive scheme to
select the regularization parameter. Moreover, using convex analysis tools, we
derive an iterative thresholding algorithm for computing the elastic-net
solution which is different from the optimization procedure originally proposed
by Zou and HastieComment: 32 pages, 3 figure
An evolutionary model for the gamma-ray system PSR J1311-3430 and its companion
The most recent member of the millisecond pulsar with very low-mass
companions and short orbital periods class, PSR J1311-3430 (Pletsch et al.
2012) is a remarkable object in various senses. Besides being the first
discovered in gamma-rays, its measured features include the very low or absent
hydrogen content. We show in this Letter that this important piece of
information leads to a very restricted range of initial periods for a given
donor mass. For that purpose, we calculate in detail the evolution of the
binary system self-consistently, including mass transfer and evaporation,
finding the features of the new evolutionary path leading to the observed
configuration. It is also important to remark that the detailed evolutionary
history of the system naturally leads to a high final pulsar mass, as it seems
to be demanded by observations.Comment: 5 pages, 5 figures, 1 table. Accepted for publication in MNRAS
Letter
Positive operator valued measures covariant with respect to an irreducible representation
Given an irreducible representation of a group G, we show that all the
covariant positive operator valued measures based on G/Z, where Z is a central
subgroup, are described by trace class, trace one positive operators.Comment: 9 pages, Latex2
Adaptive Kernel Methods Using the Balancing Principle
The regularization parameter choice is a fundamental problem in supervised learning since the performance of most algorithms crucially depends on the choice of one or more of such parameters. In particular a main theoretical issue regards the amount of prior knowledge on the problem needed to suitably choose the regularization parameter and obtain learning rates. In this paper we present a strategy, the balancing principle, to choose the regularization parameter without knowledge of the regularity of the target function. Such a choice adaptively achieves the best error rate. Our main result applies to regularization algorithms in reproducing kernel Hilbert space with the square loss, though we also study how a similar principle can be used in other situations. As a straightforward corollary we can immediately derive adaptive parameter choice for various kernel methods recently studied. Numerical experiments with the proposed parameter choice rules are also presented
Local Spatio-Temporal Representation Using the 3D Shearlet Transform (STSIP)
In this work we address the problem of analyzing video sequences and of representing meaningful space-time points of interest by using the 3D shearlet transform. We introduce a local representation based on shearlet coe cients of the video, regarded as 2D+T signal. This representation turns out to be informative to understand the local spatio-temporal characteristics, which can be easily detected by an unsupervised clustering algorithm
Group Theoretical Quantum Tomography
The paper is devoted to the mathematical foundation of the quantum tomography
using the theory of square-integrable representations of unimodular Lie groups.Comment: 13 pages, no figure, Latex2e. Submitted to J.Math.Phy
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