Simultaneous regression shrinkage , variable selection and clustering of predictors with OSCAR
Simultaneous regression shrinkage , variable selection and clustering of predictors with OSCAR
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发表时间：
2006
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通讯作者：
H. Bondell;B. Reich
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作者：
H. Bondell;B. Reich
在本文中，一种新的方法被称为OSCAR（八角收缩和聚类算法回归），提出了同时选择变量，并在线性回归的背景下进行监督聚类。该技术是基于惩罚最小二乘法与几何直观的惩罚函数，像LASSO惩罚，缩小一些系数正好为零。此外，该惩罚产生某些系数的精确相等，从而鼓励对响应具有类似影响的相关预测因子形成由单个系数表示的聚类。然后可以进一步研究这些产生的集群，以发现是什么导致了具有类似行为的群体。然后，OSCAR就模型中唯一系数的数量而言具有稀疏性。所提出的方法相比，现有的收缩和变量选择技术的预测误差和降低模型的复杂性。
In this paper, a new method called the OSCAR (Octagonal Shrinkage and Clustering Algorithm for Regression) is proposed to simultaneously select variables and perform supervised clustering in the context of linear regression. The technique is based on penalized least squares with a geometrically intuitive penalty function that, like the LASSO penalty, shrinks some coefficients to exactly zero. Additionally, this penalty yields exact equality of some coefficients, encouraging correlated predictors that have a similar effect on the response to form clusters represented by a single coefficient. These resulting clusters can then be investigated further to discover what contributes to the group having a similar behavior. The OSCAR then enjoys sparseness in terms of the number of unique coefficients in the model. The proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and reduced model complexity.