4,990 research outputs found
A Statistical Perspective on Algorithmic Leveraging
One popular method for dealing with large-scale data sets is sampling. For
example, by using the empirical statistical leverage scores as an importance
sampling distribution, the method of algorithmic leveraging samples and
rescales rows/columns of data matrices to reduce the data size before
performing computations on the subproblem. This method has been successful in
improving computational efficiency of algorithms for matrix problems such as
least-squares approximation, least absolute deviations approximation, and
low-rank matrix approximation. Existing work has focused on algorithmic issues
such as worst-case running times and numerical issues associated with providing
high-quality implementations, but none of it addresses statistical aspects of
this method.
In this paper, we provide a simple yet effective framework to evaluate the
statistical properties of algorithmic leveraging in the context of estimating
parameters in a linear regression model with a fixed number of predictors. We
show that from the statistical perspective of bias and variance, neither
leverage-based sampling nor uniform sampling dominates the other. This result
is particularly striking, given the well-known result that, from the
algorithmic perspective of worst-case analysis, leverage-based sampling
provides uniformly superior worst-case algorithmic results, when compared with
uniform sampling. Based on these theoretical results, we propose and analyze
two new leveraging algorithms. A detailed empirical evaluation of existing
leverage-based methods as well as these two new methods is carried out on both
synthetic and real data sets. The empirical results indicate that our theory is
a good predictor of practical performance of existing and new leverage-based
algorithms and that the new algorithms achieve improved performance.Comment: 44 pages, 17 figure
FDserver: A web service for protein folding research
*Summary:* To facilitate the study of protein folding, we have developed a web service for protein folding rate and folding type prediction as well as for the calculation of a variety of topological parameters of protein structure, which is freely available to the community.
*Availability:* http://sdbi.sdut.edu.cn/FDserve
Photon-assisted Fano Resonance and Corresponding Shot-Noise in a Quantum Dot
We have studied the Fano resonance in photon-assisted transport in a quantum
dot and calculated both the coherent current and spectral density of shot
noise. It is predicted, for the first time, that the shape of Fano profile will
also appear in satellite peaks. It is found that the variations of Fano
profiles with the strengths of nonresonant transmissions are not synchronous in
absorption and emission sidebands. The effect of interference on
photon-assisted pumped current has been also investigated. We further predict
the current and spectral density of shot noise as a function of the phase,
which exhibits an intrinsic property of resonant and nonresonant channels in
the structures.Comment: 4 pages, 5 figure
Investigating the topological structure of quenched lattice QCD with overlap fermions by using multi-probing approximation
The topological charge density and topological susceptibility are determined
by multi-probing approximation using overlap fermions in quenched SU(3) gauge
theory. Then we investigate the topological structure of the quenched QCD
vacuum, and compare it with results from the all-scale topological density, the
results are consistent. Random permuted topological charge density is used to
check whether these structures represent underlying ordered properties.
Pseudoscalar glueball mass is extracted from the two-point correlation function
of the topological charge density. We study ensembles of different lattice
spacing with the same lattice volume , the results are
compatible with the results of all-scale topological charge density, and the
topological structures revealed by multi-probing are much closer to all-scale
topological charge density than that by eigenmode expansion.Comment: 12 pages,34 figure
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