PATHWISE COORDINATE OPTIMIZATION
PATHWISE COORDINATE OPTIMIZATION
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DOI：
10.1214/07-aoas131
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发表时间：
2007-12-01
影响因子：
1.8
通讯作者：
Tibshirani, Robert
中科院分区：
文献类型：
--
作者：
Friedman, Jerome;Hastie, Trevor;Tibshirani, Robert
我们考虑了一类凸优化问题的“一次一次”坐标智能下降算法。在文献中已经提出了这种算法用于l -1惩罚回归（lasso），但它似乎在很大程度上被忽视了。确实。在凸优化中，坐标算法似乎并不常用。结果表明，该算法在求解大型套索问题时，与著名的LARS（或同伦）方法相比，具有很强的竞争力，并可应用于garotte和弹性网等相关方法。然而，事实证明，在“融合套索”中，坐标智能下降并不起作用。因此，我们推导出一种广义算法，该算法比标准凸优化器在更短的时间内产生解。最后。我们将该方法推广到二维融合套索，并在一些图像平滑问题上证明了它的性能。
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 (hat 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 call 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 oil some image smoothing problems.