Pathwise coordinate optimization

Details Pathwise coordinate optimization Pathwise coordinate optimization

2007-08-10

arxiv.org/abs/0708.1485v2

Annals of Applied Statistics 2007, Vol. 1, No. 2, 302-332

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Published in at http://dx.doi.org/10.1214/07-AOAS131 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/07-AOAS131

We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have been largely ignored. Indeed, it seems that coordinate-wise algorithms are not often used in convex optimization. We show that this algorithm is very competitive with the well-known LARS (or homotopy) procedure in large lasso problems, and that it can be applied to related methods such as the garotte and elastic net. It turns out that coordinate-wise descent does not work in the ``fused lasso,'' however, so we derive a generalized algorithm that yields the solution in much less time that a standard convex optimizer. Finally, we generalize the procedure to the two-dimensional fused lasso, and demonstrate its performance on some image smoothing problems.

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