2,015 research outputs found
Structured variable selection in support vector machines
When applying the support vector machine (SVM) to high-dimensional
classification problems, we often impose a sparse structure in the SVM to
eliminate the influences of the irrelevant predictors. The lasso and other
variable selection techniques have been successfully used in the SVM to perform
automatic variable selection. In some problems, there is a natural hierarchical
structure among the variables. Thus, in order to have an interpretable SVM
classifier, it is important to respect the heredity principle when enforcing
the sparsity in the SVM. Many variable selection methods, however, do not
respect the heredity principle. In this paper we enforce both sparsity and the
heredity principle in the SVM by using the so-called structured variable
selection (SVS) framework originally proposed in Yuan, Joseph and Zou (2007).
We minimize the empirical hinge loss under a set of linear inequality
constraints and a lasso-type penalty. The solution always obeys the desired
heredity principle and enjoys sparsity. The new SVM classifier can be
efficiently fitted, because the optimization problem is a linear program.
Another contribution of this work is to present a nonparametric extension of
the SVS framework, and we propose nonparametric heredity SVMs. Simulated and
real data are used to illustrate the merits of the proposed method.Comment: Published in at http://dx.doi.org/10.1214/07-EJS125 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Structured variable selection and estimation
In linear regression problems with related predictors, it is desirable to do
variable selection and estimation by maintaining the hierarchical or structural
relationships among predictors. In this paper we propose non-negative garrote
methods that can naturally incorporate such relationships defined through
effect heredity principles or marginality principles. We show that the methods
are very easy to compute and enjoy nice theoretical properties. We also show
that the methods can be easily extended to deal with more general regression
problems such as generalized linear models. Simulations and real examples are
used to illustrate the merits of the proposed methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS254 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Composite quantile regression and the oracle Model Selection Theory
Coefficient estimation and variable selection in multiple linear regression
is routinely done in the (penalized) least squares (LS) framework. The concept
of model selection oracle introduced by Fan and Li [J. Amer. Statist. Assoc. 96
(2001) 1348--1360] characterizes the optimal behavior of a model selection
procedure. However, the least-squares oracle theory breaks down if the error
variance is infinite. In the current paper we propose a new regression method
called composite quantile regression (CQR). We show that the oracle model
selection theory using the CQR oracle works beautifully even when the error
variance is infinite. We develop a new oracular procedure to achieve the
optimal properties of the CQR oracle. When the error variance is finite, CQR
still enjoys great advantages in terms of estimation efficiency. We show that
the relative efficiency of CQR compared to the least squares is greater than
70% regardless the error distribution. Moreover, CQR could be much more
efficient and sometimes arbitrarily more efficient than the least squares. The
same conclusions hold when comparing a CQR-oracular estimator with a
LS-oracular estimator.Comment: Published in at http://dx.doi.org/10.1214/07-AOS507 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Direct Approach to Sparse Discriminant Analysis in Ultra-high Dimensions
1 online resource (PDF, 27 pages
Upregulation of Mitochondrial Uncoupling Protein-2 by the AMP-Activated Protein Kinase in Endothelial Cells Attenuates Oxidative Stress in Diabetes
OBJECTIVE—Recent evidence suggests that the AMP-activated protein kinase (AMPK) is an important therapeutic target for diabetes. The present study was conducted to determine how AMPK activation suppressed tyrosine nitration of prostacyclin synthase in diabetes
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