# Safe Feature Elimination in Sparse Supervised Learning

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-126.pdf

We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of variables prior to running the supervised learning algorithm. The methods are not heuristic: they only eliminate features that are {\em guaranteed} to be absent after solving the learning problem. Our framework applies to a large class of problems, including support vector machine classification, logistic regression and least-squares. The complexity of the feature elimination step is negligible compared to the typical computational effort involved in the sparse supervised learning problem: it grows linearly with the number of features times the number of examples, with much better count if data is sparse. We apply our method to data sets arising in text classification and observe a dramatic reduction of the dimensionality, hence in computational effort required to solve the learning problem, especially when very sparse classifiers are sought. Our method allows to immediately extend the scope of existing algorithms, allowing us to run them on data sets of sizes that were out of their reach before.

BibTeX citation:

@techreport{El Ghaoui:EECS-2010-126,
Author = {El Ghaoui, Laurent and Viallon, Vivian and Rabbani, Tarek},
Title = {Safe Feature Elimination in Sparse Supervised Learning},
Institution = {EECS Department, University of California, Berkeley},
Year = {2010},
Month = {Sep},
URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-126.html},
Number = {UCB/EECS-2010-126},
Abstract = {We investigate fast methods that allow to quickly eliminate variables
(features) in supervised learning problems involving a convex loss
function and a $l_1$-norm penalty, leading to a
potentially substantial reduction in the number of variables prior to running
the supervised learning algorithm. The methods are not heuristic:
they only eliminate features that are {\em guaranteed} to
be absent after solving the learning problem. Our framework applies to a
large class of problems, including support vector machine
classification, logistic regression and least-squares.

The complexity of the feature elimination step is negligible
compared to the typical computational effort involved in the
sparse supervised learning problem: it grows linearly with the
number of features times the number of examples, with much better
count if data is sparse.  We apply our method to data sets arising
in text classification and observe a dramatic reduction of the
dimensionality, hence in computational effort required to solve
the learning problem, especially when very sparse classifiers are
sought. Our method allows to immediately extend the scope of
existing algorithms, allowing us to run them on data sets of sizes
that were out of their reach before.}
}


EndNote citation:

%0 Report
%A El Ghaoui, Laurent
%A Viallon, Vivian
%A Rabbani, Tarek
%T Safe Feature Elimination in Sparse Supervised Learning
%I EECS Department, University of California, Berkeley
%D 2010
%8 September 21
%@ UCB/EECS-2010-126
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-126.html
%F El Ghaoui:EECS-2010-126