## Dept. of Mathematics and Computer Science (Berlin)

Your review has been received.

**Thank you very much.**

**reviewer:** Miloslav Znojil
**reviewernum:** 9689

**revieweremail:** znojil@ujf.cas.cz

**zblno:** DE015066134

**author:** Osborne, M. R.; Presnell, Brett; Turlach, B. A.:

**shorttitle:** Selection of variables in least squares problems

**source:** IMA J. Numer. Anal. 20, No. 3, 389 - 403 (2000).

**rpclass:** 65F20

**rsclass:** 65F35; 55Q52; 62J12; 91B44

**keywords:** exploratory data analysis, design matrix, selection of columns, stepwise regression, minimal sum of squares of residuals, selection mechanisms, homotopy method, descent method

**revtext:**
The least square technique of solving a large non-homogeneous
linear algebraic set is considered within the so called Lasso
approach reducing the set of variables (columns of the matrix).
The ``non-smooth" constraint (demanding that the $\ell_1$ norm of
the solution vector $x$ is smaller than a constant $\kappa$) has a
useful property of forcing components of $x$ to zero when $\kappa$
is small, but precisely this requirement makes the problem
complicated.
The paper introduces and studies the two complementary methods.
Both of them have a finite termination property and both of them
may find an efficient implementation via a modified Gram-Schmidt
orthogonalization. One of them (a compact descent method) can
operate as a probe at a particular $\kappa$, the other one (viz.,
homotopy method) is capable to describe the possible selection
regimes globally.

review-form Generator ()

Written by
*
Michael Jost* (jo@zblmath.FIZ-Karlsruhe.DE).