In a multiple regression with grouped predictors, it is usually desired to select important groups as well as to select important variables within a group simultaneously. To achieve this so-called “bi-level selection,” group bridge has been developed as a combination of group-level bridge and variable-level lasso penalties. However, in many scientific areas, prior knowledge is available about the importance of certain groups of predictors, leading to the necessity of methodological development to incorporate such valuable information. For a prior-informative group, we propose a new penalty called “group ridge” as a combination of grouplevel ridge and variable-level lasso penalties, which always preserves this group while selects important variables in it. Then, we propose a composite group penalization named “prior group bridge” by applying group ridge and group bridge to prior-informative groups and groups with no prior information, respectively. We prove that prior group bridge achieves estimation and group selection consistencies given that the prior information is correct. In addition, we demonstrate the empirical advantage of prior group bridge over group bridge in terms of estimation, group and variable selection, and prediction through simulation studies. Finally, we apply prior group bridge to a genetic association study of bipolar disorder to illustrate its applicability and efficacy in real applications.

中文翻译：

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通过先验组桥方法将先验信息进行分组变量选择

在具有分组预测变量的多元回归中，通常需要选择重要的组以及同时选择组内的重要变量。为了实现这种所谓的“双级选择”，已经开发了组桥作为组级桥和可变级套索惩罚的组合。但是，在许多科学领域中，已有关于某些预测变量组重要性的先验知识，这导致需要进行方法学开发以纳入此类有价值的信息。对于具有先验信息的组，我们提出了一种新的惩罚，称为“组岭”，它是组级岭和可变级套索惩罚的组合，在选择重要变量时始终保留该组。然后，我们通过将组脊和组桥分别应用于先验信息组和没有先验信息的组，提出了一种称为“先有组桥”的综合组惩罚。我们证明，在先验信息正确的情况下，先验组桥可以实现估计和组选择一致性。此外，我们通过仿真研究证明了先验组桥相对于组桥的经验优势，即在估计，组和变量选择以及预测方面。最后，我们将先前的桥梁应用于双相情感障碍的遗传关联研究，以说明其在实际应用中的适用性和有效性。我们证明，在先验信息正确的情况下，先验组桥可以实现估计和组选择一致性。此外，我们通过仿真研究证明了先验组桥相对于组桥的经验优势，即在估计，组和变量选择以及预测方面。最后，我们将先前的桥梁应用于双相情感障碍的遗传关联研究，以说明其在实际应用中的适用性和有效性。我们证明，在先验信息正确的情况下，先验组桥可以实现估计和组选择一致性。此外，我们通过仿真研究证明了先验组桥相对于组桥在经验估计，组和变量选择以及预测方面的经验优势。最后，我们将先前的桥梁应用到躁郁症的遗传关联研究中，以说明其在实际应用中的适用性和有效性。