@CONFERENCE\{IMM2007-05254,
author = "M. M{\o}rup and L. H. Clemmensen",
title = "Multiplicative updates for the {LASSO}",
year = "2007",
booktitle = "Machine Learning for Signal Processing (MLSP), {IEEE} Workshop on",
volume = "",
series = "",
editor = "",
publisher = "",
organization = "",
address = "",
url = "http://www2.imm.dtu.dk/pubdb/p.php?5254",
abstract = "Multiplicative updates have proven useful for non-negativity
constrained optimization. Presently, we demonstrate how
multiplicative updates also can be used for unconstrained
optimization. This is for instance useful when estimating the
least absolute shrinkage and selection operator (LASSO), i.e.
least squares minimization with \$L\_1\$-norm regularization, since
the multiplicative updates (MU) can efficiently exploit the
structure of the problem traditionally solved using quadratic
programming (QP). We derive an algorithm based on {MU} for the {LASSO}
and compare the performance to Matlabs standard {QP} solver as well
as the basis pursuit denoising algorithm (BP) which can be
obtained from
www.sparselab.stanford.edu. The algorithms were tested on three
benchmark bio-informatic datasets: A small scale data set where
the number of observations is larger than the number of variables
estimated (\$M