The adaptive lasso and its oracle properties
The adaptive lasso and its oracle properties
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DOI：
10.1198/016214506000000735
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发表时间：
2006-12-01
影响因子：
3.7
通讯作者：
Zou, Hui
中科院分区：
文献类型：
--
作者：
Zou, Hui
套索是同时估计和变量选择的流行技术。Lasso变量选择已被证明在某些条件下是一致的。在这项工作中，我们推导出一个必要条件的套索变量选择是一致的。因此，在某些情况下，套索对于变量选择是不一致的。然后，我们提出了一个新版本的套索，称为自适应套索，其中自适应权重用于惩罚l（1）惩罚中的不同系数。我们表明，自适应套索享有的预言属性，即，它执行以及如果真正的基础模型是预先给定的。类似的套索，自适应套索被证明是近极大极小最优。此外，自适应套索可以通过用于求解套索的相同有效算法来求解。我们还讨论了自适应套索在广义线性模型中的推广，并证明了预言性质在弱正则性条件下仍然成立。作为我们的理论的副产品，非负的加洛特被证明是一致的变量选择。
The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain scenarios where the lasso is inconsistent for variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the l(1) penalty. We show that the adaptive lasso enjoys the oracle properties; namely, it performs as well as if the true underlying model were given in advance. Similar to the lasso, the adaptive lasso is shown to be near-minimax optimal. Furthermore, the adaptive lasso can be solved by the same efficient algorithm for solving the lasso. We also discuss the extension of the adaptive lasso in generalized linear models and show that the oracle properties still hold under mild regularity conditions. As a byproduct of our theory, the nonnegative garotte is shown to be consistent for variable selection.