3,603 research outputs found
Optimal selection of reduced rank estimators of high-dimensional matrices
We introduce a new criterion, the Rank Selection Criterion (RSC), for
selecting the optimal reduced rank estimator of the coefficient matrix in
multivariate response regression models. The corresponding RSC estimator
minimizes the Frobenius norm of the fit plus a regularization term proportional
to the number of parameters in the reduced rank model. The rank of the RSC
estimator provides a consistent estimator of the rank of the coefficient
matrix; in general, the rank of our estimator is a consistent estimate of the
effective rank, which we define to be the number of singular values of the
target matrix that are appropriately large. The consistency results are valid
not only in the classic asymptotic regime, when , the number of responses,
and , the number of predictors, stay bounded, and , the number of
observations, grows, but also when either, or both, and grow, possibly
much faster than . We establish minimax optimal bounds on the mean squared
errors of our estimators. Our finite sample performance bounds for the RSC
estimator show that it achieves the optimal balance between the approximation
error and the penalty term. Furthermore, our procedure has very low
computational complexity, linear in the number of candidate models, making it
particularly appealing for large scale problems. We contrast our estimator with
the nuclear norm penalized least squares (NNP) estimator, which has an
inherently higher computational complexity than RSC, for multivariate
regression models. We show that NNP has estimation properties similar to those
of RSC, albeit under stronger conditions. However, it is not as parsimonious as
RSC. We offer a simple correction of the NNP estimator which leads to
consistent rank estimation.Comment: Published in at http://dx.doi.org/10.1214/11-AOS876 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org) (some typos corrected
Observation of a push force on the end face of a nm fiber taper exerted by outgoing light
There are two different proposals for the momentum of light in a transparent
dielectric of refractive index n: Minkowski's version nE/c and Abrahm's version
E/(nc), where E and c are the energy and vacuum speed of light, respectively.
Despite many tests and debates over nearly a century, momentum of light in a
transparent dielectric remains controversial. In this Letter, we report a
direct observation of the inward push force on the end face of a free nm fiber
taper exerted by the outgoing light. Our results clearly support Abraham
momentum. Our experiment also indicates an inward surface pressure on a
dielectric exerted by the incident light, different from the commonly
recognized pressure due to the specular reflection. Such an inward surface
pressure by the incident light may be useful for precise design of the
laser-induced inertially-confined fusion.Comment: 9 pages, 3 figures;Accepted for publication as a Letter in Physical
Review Letters(CODE: LP11093
Pacifying the Fermi-liquid: battling the devious fermion signs
The fermion sign problem is studied in the path integral formalism. The
standard picture of Fermi liquids is first critically analyzed, pointing out
some of its rather peculiar properties. The insightful work of Ceperley in
constructing fermionic path integrals in terms of constrained world-lines is
then reviewed. In this representation, the minus signs associated with
Fermi-Dirac statistics are self consistently translated into a geometrical
constraint structure (the {\em nodal hypersurface}) acting on an effective
bosonic dynamics. As an illustrative example we use this formalism to study
1+1-dimensional systems, where statistics are irrelevant, and hence the sign
problem can be circumvented. In this low-dimensional example, the structure of
the nodal constraints leads to a lucid picture of the entropic interaction
essential to one-dimensional physics. Working with the path integral in
momentum space, we then show that the Fermi gas can be understood by analogy to
a Mott insulator in a harmonic trap. Going back to real space, we discuss the
topological properties of the nodal cells, and suggest a new holographic
conjecture relating Fermi liquids in higher dimensions to soft-core bosons in
one dimension. We also discuss some possible connections between mixed
Bose/Fermi systems and supersymmetry.Comment: 28 pages, 5 figure
Joint variable and rank selection for parsimonious estimation of high-dimensional matrices
We propose dimension reduction methods for sparse, high-dimensional
multivariate response regression models. Both the number of responses and that
of the predictors may exceed the sample size. Sometimes viewed as
complementary, predictor selection and rank reduction are the most popular
strategies for obtaining lower-dimensional approximations of the parameter
matrix in such models. We show in this article that important gains in
prediction accuracy can be obtained by considering them jointly. We motivate a
new class of sparse multivariate regression models, in which the coefficient
matrix has low rank and zero rows or can be well approximated by such a matrix.
Next, we introduce estimators that are based on penalized least squares, with
novel penalties that impose simultaneous row and rank restrictions on the
coefficient matrix. We prove that these estimators indeed adapt to the unknown
matrix sparsity and have fast rates of convergence. We support our theoretical
results with an extensive simulation study and two data analyses.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1039 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Improved Storage Security using IDS and Performance using Container De-Duplication
Due to enormous increase in use of web services in our day today life, web services have moved to multitier design where in web server runs the application front-end logic and data are outsourced to a database or file server. In our system, we will implement secure de-duplication which is a technique for eliminating duplicate copies of data, it has been largely used in cloud storage to reduce storage space and upload bandwidth with Container security, an IDS system that models the network acts as user sessions across both front-end web server and back-end database. By monitoring both the web and subsequent database requests, we are capable to search out attacks that an independent Intrusion Detection System (IDS) unable to identify. In this system, each user requesting for our application will be allocated separate container. The container based web architecture not only fasters profiling of causal mapping, but it also provides an isolation that obstruct future session hijacking attacks .Each user will hold de-key which is a new construction in which users do not require to manage any keys on their own but as an alternative securely distribute the convergent key shares across multiple servers. We implement De-key to demonstrate that De-key incurs limited overhead in realistic environments
Universal statistics of non-linear energy transfer in turbulent models
A class of shell models for turbulent energy transfer at varying the
inter-shell separation, , is investigated. Intermittent corrections in
the continuous limit of infinitely close shells () have
been measured. Although the model becomes, in this limit, non-intermittent, we
found universal aspects of the velocity statistics which can be interpreted in
the framework of log-poisson distributions, as proposed by She and Waymire
(1995, Phys. Rev. Lett. 74, 262). We suggest that non-universal aspects of
intermittency can be adsorbed in the parameters describing statistics and
properties of the most singular structure. On the other hand, universal aspects
can be found by looking at corrections to the monofractal scaling of the most
singular structure. Connections with similar results reported in other shell
models investigations and in real turbulent flows are discussed.Comment: 4 pages, 2 figures available upon request to [email protected]
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