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On the grouped selection and model complexity of the adaptive elastic net

机译：自适应弹性网的分组选择与模型复杂度

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摘要

Lasso proved to be an extremely successful technique for simultaneous estimation and variable selection. However lasso has two major drawbacks. First, it does not enforce any grouping effect and secondly in some situation lasso solutions are inconsistent for variable selection. To overcome this inconsistency adaptive lasso is proposed where adaptive weights are used for penalizing different coefficients. Recently a doubly regularized technique namely elastic net is proposed which encourages grouping effect i.e. either selection or omission of the correlated variables together. However elastic net is also inconsistent. In this paper we study adaptive elastic net which does not have this drawback. In this article we specially focus on the grouped selection property of adaptive elastic net along with its model selection complexity. We also shed some light on the bias-variance tradeoff of different regularization methods including adaptive elastic net. An efficient algorithm was proposed in the line of LARS-EN, which is then illustrated with simulated as well as real life data examples.
机译：套索被证明是同时进行估计和变量选择的一种非常成功的技术。但是套索有两个主要缺点。首先，它不执行任何分组效果，其次，在某些情况下，套索解决方案对于变量选择而言是不一致的。为了克服这种不一致，提出了自适应套索，其中自适应权重用于惩罚不同的系数。最近，提出了一种双重正则化技术，即弹性网，其鼓励分组效应，即相关变量的选择或省略。但是，弹性网也不一致。在本文中，我们研究了没有此缺点的自适应弹性网。在本文中，我们特别关注自适应弹性网的分组选择属性及其模型选择的复杂性。我们还阐明了包括自适应弹性网在内的不同正则化方法的偏差方差折衷。在LARS-EN方面提出了一种有效的算法，然后通过仿真和实际数据示例进行了说明。

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