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Hui Zou and Trevor Hastie answers a
few questions about this month's fast breaking paper in
the field of Mathematics.
From
•>>October 2006
Field:
Mathematics
Article Title: Regularization and variable selection via the elastic net
Authors: Zou, H;Hastie, T
Journal: J ROY STAT SOC SER B-STAT MET
Volume: 67
Issue:
Page: :301-320
Year: Part 2 2005
* Stanford Univ, Dept Stat, Stanford, CA 94305 USA.
* Stanford Univ, Dept Stat, Stanford, CA 94305 USA.
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 Why
do you think your paper is highly cited?
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“The method described
in our paper is currently used by researchers in pharmaceutical companies (such as
GlaxoSmithKline) to do biomarker
selection and choose risk factors in clinical data.”
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The problem of variable selection in high dimensions is of
great interest to statisticians, biologists, and researchers in
other fields. Our elastic net is an elegant solution to this
problem, especially when the variables occur in groups. We
implemented the elastic net in R, a free software package
distributed on CRAN, which has made the method available to
interested readers.
Does
it describe a new discovery, methodology, or synthesis of
knowledge?
Our paper introduced a new regularization technique (the
elastic net) for solving the variable selection problem in
predictive modeling with high-dimensional predictors.
Could
you summarize the significance of your paper in layman’s terms?
In high-dimensional data analysis, the number of variables
can greatly exceed the number of observations, and often strong
correlations exist among subsets of variables. As a result, many
existing variable selection methods perform poorly in the
high-dimensional setting. Our main contribution is to show a
novel way to combine the strengths of L2 regularization and L1
minimization with an appealing method—the elastic net—that
elegantly handles these two issues. The elastic net is
especially useful in the "large p small n setting," as
is the case for microarray data.
How
did you become involved in this research, and were any problems
encountered along the way?
Our work was motivated by the gene selection problem in
microarray data analysis. We first applied "the
lasso," a method for regularizing least squares regression
via L1 constraints, invented by Professor Robert Tibshirani, to
microarray data, but the results were not very satisfactory.
Luckily for us, the "Least Angle Regression" paper
by B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani (Annals
of Statistics 32(2): 407-451, 2004) helped us understand the
mechanism of the lasso selection. We then turned our attention
to figuring out ways to improve the lasso and came up with the
elastic net idea.
Are
there any social or political implications for your research?
The method described in our paper is currently used by
researchers in pharmaceutical companies, such as GlaxoSmithKline,
to do biomarker selection and choose risk factors in clinical
data.
Hui Zou, Ph.D.
Assistant Professor
School of Statistics
University of Minnesota
Minneapolis, MN, USA
Trevor Hastie, Ph.D.
Professor
Department of Statistics
Stanford University
Stanford, CA, USA
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ESI Special Topics,
October 2006
Citing URL - http://www.esi-topics.com/fbp/2006/october06-Zou_Hastie.html
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