线性回归中组套索和稀疏组套索的精确分块优化
机器学习
2010-11-12 v2
摘要
组套索是一种惩罚回归方法，用于协变量被划分为组的回归问题，以促进组级别的稀疏性。现有的寻找组套索估计量的方法要么使用梯度投影方法在每一步同时更新整个系数向量，要么一次更新一组系数，使用不精确线搜索来近似当所有其他组系数固定时该组系数的最优值。我们提出了一种新的线性回归情况下组套索的计算方法——单线搜索（SLS）算法，该算法通过一次单变量线搜索来计算每组（当所有其他系数固定时）的精确最优值。我们进行了模拟，证明SLS算法通常比现有的计算方法更高效。我们还通过有符号单线搜索（SSLS）算法将SLS算法扩展到稀疏组套索问题，并给出了支持这两种算法的理论结果。
引用
@article{arxiv.1010.3320,
title = {Exact block-wise optimization in group lasso and sparse group lasso for linear regression},
author = {Rina Foygel and Mathias Drton},
journal= {arXiv preprint arXiv:1010.3320},
year = {2010}
}
备注
We have been made aware of the earlier work by Puig et al. (2009) which derives the same result for the (non-sparse) group lasso setting. We leave this manuscript available as a technical report, to serve as a reference for the previously untreated sparse group lasso case, and for timing comparisons of various methods in the group lasso setting. The manuscript is updated to include this reference