397 research outputs found
Variable selection for the multicategory SVM via adaptive sup-norm regularization
The Support Vector Machine (SVM) is a popular classification paradigm in
machine learning and has achieved great success in real applications. However,
the standard SVM can not select variables automatically and therefore its
solution typically utilizes all the input variables without discrimination.
This makes it difficult to identify important predictor variables, which is
often one of the primary goals in data analysis. In this paper, we propose two
novel types of regularization in the context of the multicategory SVM (MSVM)
for simultaneous classification and variable selection. The MSVM generally
requires estimation of multiple discriminating functions and applies the argmax
rule for prediction. For each individual variable, we propose to characterize
its importance by the supnorm of its coefficient vector associated with
different functions, and then minimize the MSVM hinge loss function subject to
a penalty on the sum of supnorms. To further improve the supnorm penalty, we
propose the adaptive regularization, which allows different weights imposed on
different variables according to their relative importance. Both types of
regularization automate variable selection in the process of building
classifiers, and lead to sparse multi-classifiers with enhanced
interpretability and improved accuracy, especially for high dimensional low
sample size data. One big advantage of the supnorm penalty is its easy
implementation via standard linear programming. Several simulated examples and
one real gene data analysis demonstrate the outstanding performance of the
adaptive supnorm penalty in various data settings.Comment: Published in at http://dx.doi.org/10.1214/08-EJS122 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Empirical Evaluation of Test Coverage for Functional Programs
The correlation between test coverage and test effectiveness is important to justify the use of coverage in practice. Existing results on imperative programs mostly show that test coverage predicates effectiveness. However, since functional programs are usually structurally different from imperative ones, it is unclear whether the same result may be derived and coverage can be used as a prediction of effectiveness on functional programs. In this paper we report the first empirical study on the correlation between test coverage and test effectiveness on functional programs. We consider four types of coverage: as input coverages, statement/branch coverage and expression coverage, and as oracle coverages, count of assertions and checked coverage. We also consider two types of effectiveness: raw effectiveness and normalized effectiveness. Our results are twofold. (1) In general the findings on imperative programs still hold on functional programs, warranting the use of coverage in practice. (2) On specific coverage criteria, the results may be unexpected or different from the imperative ones, calling for further studies on functional programs
Higher-order multi-scale method for high-accuracy nonlinear thermo-mechanical simulation of heterogeneous shells
In the present work, we consider multi-scale computation and convergence for
nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells
possessing temperature-dependent material properties and orthogonal periodic
configurations. The first contribution is that a novel higher-order macro-micro
coupled computational model is rigorously devised via multi-scale asymptotic
technique and Taylor series approach for high-accuracy simulation of
heterogeneous shells. Benefitting from the higher-order corrected terms, the
higher-order multi-scale computational model keeps the conservation of local
energy and momentum for nonlinear thermo-mechanical simulation. Moreover, a
global error estimation with explicit rate of higher-order multi-scale
solutions is first derived in the energy norm sense. Furthermore, an efficient
space-time numerical algorithm with off-line and on-line stages is presented in
detail. Adequate numerical experiments are conducted to confirm the competitive
advantages of the presented multi-scale approach, exhibiting not only the
exceptional numerical accuracy, but also the less computational expense for
heterogeneous shells
Quantum Hall Effect in Bernal Stacked and Twisted Bilayer Graphene Grown on Cu by Chemical Vapor Deposition
We examine the quantum Hall effect in bilayer graphene grown on Cu substrates
by chemical vapor deposition. Spatially resolved Raman spectroscopy suggests a
mixture of Bernal (A-B) stacked and rotationally faulted (twisted) domains.
Magnetotransport measurements performed on bilayer domains with a wide 2D band
reveal quantum Hall states (QHSs) at filling factors consistent
with a Bernal stacked bilayer, while magnetotransport measurements in bilayer
domains defined by a narrow 2D band show a superposition of QHSs of two
independent monolayers. The analysis of the Shubnikov-de Haas oscillations
measured in twisted graphene bilayers provides the carrier density in each
layer as a function of the gate bias and the inter-layer capacitance.Comment: 5 pages, 4 figure
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Methods of forming graphene single crystal domains on a low nucleation site density substrate
A method of forming graphene single crystal domains on a carbon substrate is described.Board of Regents, University of Texas Syste
Self-optimization wavelet-learning method for predicting nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations
In the present work, we propose a self-optimization wavelet-learning method
(SO-W-LM) with high accuracy and efficiency to compute the equivalent nonlinear
thermal conductivity of highly heterogeneous materials with randomly
hierarchical configurations. The randomly structural heterogeneity,
temperature-dependent nonlinearity and material property uncertainty of
heterogeneous materials are considered within the proposed self-optimization
wavelet-learning framework. Firstly, meso- and micro-structural modeling of
random heterogeneous materials are achieved by the proposed computer
representation method, whose simulated hierarchical configurations have
relatively high volume ratio of material inclusions. Moreover,
temperature-dependent nonlinearity and material property uncertainties of
random heterogeneous materials are modeled by a polynomial nonlinear model and
Weibull probabilistic model, which can closely resemble actual material
properties of heterogeneous materials. Secondly, an innovative stochastic
three-scale homogenized method (STSHM) is developed to compute the macroscopic
nonlinear thermal conductivity of random heterogeneous materials. Background
meshing and filling techniques are devised to extract geometry and material
features of random heterogeneous materials for establishing material databases.
Thirdly, high-dimensional and highly nonlinear material features of material
databases are preprocessed and reduced by wavelet decomposition technique. The
neural networks are further employed to excavate the predictive models from
dimension-reduced low-dimensional data
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