Using Generalized Correlation to Effect Variable Selection in Very High Dimensional Problems
Using Generalized Correlation to Effect Variable Selection in Very High Dimensional Problems
复制标题
DOI：
10.1198/jcgs.2009.08041
复制
发表时间：
2009-09-01
影响因子：
2.4
通讯作者：
Miller, Hugh
中科院分区：
文献类型：
--
作者：
Hall, Peter;Miller, Hugh
在某些情况下，使用传统的线性模型实现变量选择可以非常有效地执行，只要对相关组件的响应近似单调，并且其梯度变化仅缓慢。在其他情况下，响应的非线性可能会导致大量的矢量成分被忽略。即使通过线性模型拟合获得良好的结果，有时也可以通过使用非线性方法来改善它们。这些情况在实践中可以通过真实的数据产生，并且可以激发替代方法。我们建议一种基于对响应变量和解释矢量组成部分之间的广义经验相关性的方法。该技术不是基于预测的，并且可以识别有影响力但不是明确的预测模型一部分的变量。我们探讨了该方法的真实和模拟数据的性能，并给出了一个理论上的参数证明其有效性。该方法还可以通过提供初步的“大规模降低”步骤，作为使用替代技术（例如自适应Lasso）的前奏，而不是与常规预测变量选择的替代方案一起使用，而不是替代传统的基于预测的变量选择。并非总是很好地应对很高的尺寸。与本文数字部分有关的补充材料可在线获得。
Using the traditional linear model to implement variable selection can perform very effectively in some cases, provided the response to relevant components is approximately monotone and its gradient changes only slowly. In other circumstances, nonlinearity of response can result in significant vector components being overlooked. Even if good results are obtained by linear model fitting, they can sometimes be bettered by using a nonlinear approach. These circumstances can arise in practice, with real data, and they motivate alternative methodologies. We suggest an approach based on ranking generalized empirical correlations between the response variable and components of the explanatory vector. This technique is not prediction-based, and can identify variables that are influential but not explicitly part of a predictive model. We explore the method's performance for real and simulated data, and give a theoretical argument demonstrating its validity. The method can also be used in conjunction with, rather than as an alternative to, conventional prediction-based variable selections, by providing a preliminary "massive dimension reduction" step as a prelude to using alternative techniques (e.g., the adaptive lasso) that do not always cope well with very high dimensions. Supplemental materials relating to the numerical sections of this paper are available online.