The Gamma Lasso
The Gamma Lasso
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伽玛套索
DOI：
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Matt Taddy
中科院分区：
文献类型：
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作者：
Matt Taddy
过去15年的统计学文献已经建立了稀疏减偏正则化的许多有利性质：可以粗略地理解为在$L_0$和$L_1$范数之间的范围内的罚函数下提供估计的技术。然而，套索L_1正则化估计仍然是工业“大数据”应用的标准工具，因为它的计算成本最小，并存在易于应用的惩罚选择规则。作为回应，本文提出了一个简单的新的算法框架，不需要更多的计算比套索路径：一步估计（POSE）的路径做$L_1$惩罚回归估计网格上的减少处罚，但适应系数特定的权重，以减少作为一个函数的系数估计在前一个路径步骤。这提供了稀疏递减偏置正则化，与最快的套索算法相比没有额外的成本。此外，我们的“伽玛套索”的POSE的实现是伴随着一个可靠的启发式的自由度的适合，使标准的信息标准可以应用于惩罚选择。我们还提供了新的结果之间的距离加权L_1 $和L_0 $惩罚预测，这使我们能够建立直觉的POSE和其他减少偏差正则化计划。在广泛的模拟和逻辑回归的应用，以评估曲棍球运动员的表现的方法和结果进行说明。
The statistics literature of the past 15 years has established many favorable properties for sparse diminishing-bias regularization: techniques which can roughly be understood as providing estimation under penalty functions spanning the range of concavity between $L_0$ and $L_1$ norms. However, lasso $L_1$-regularized estimation remains the standard tool for industrial `Big Data' applications because of its minimal computational cost and the presence of easy-to-apply rules for penalty selection. In response, this article proposes a simple new algorithm framework that requires no more computation than a lasso path: the path of one-step estimators (POSE) does $L_1$ penalized regression estimation on a grid of decreasing penalties, but adapts coefficient-specific weights to decrease as a function of the coefficient estimated in the previous path step. This provides sparse diminishing-bias regularization at no extra cost over the fastest lasso algorithms. Moreover, our `gamma lasso' implementation of POSE is accompanied by a reliable heuristic for the fit degrees of freedom, so that standard information criteria can be applied in penalty selection. We also provide novel results on the distance between weighted-$L_1$ and $L_0$ penalized predictors; this allows us to build intuition about POSE and other diminishing-bias regularization schemes. The methods and results are illustrated in extensive simulations and in application of logistic regression to evaluating the performance of hockey players.
影响因子：
4.5
作者：
Wang Z;Liu H;Zhang T
通讯作者：
Zhang T
影响因子：
1.5
作者：
Dyar, M. D.;Schaefer, M. W.;Bishop, J. L.
通讯作者：
Bishop, J. L.