Advances in Variable Selection with Grouped Predictors

这个项目在分组预测者的背景下开发变量选择程序，其中分组结构可以是已知的也可以是未知的。已知的分组结构包括方差分析(ANOVA)模型的情况，其中多个‘伪’变量代表单个因素，或者在使用基函数的非参数回归中。在这些情况下，需要将整个变量集作为一个组包括或排除。当存在对反应有综合影响的潜在预测因子簇时，就会发生未知的分组结构，例如一组共享共同路径的基因。这项研究解决了已知和未知分组结构下的变量选择问题，同时解决了针对手头问题的额外目标。该项目的第一个组成部分是将“监督聚类”和变量选择合并为一个步骤，以便于在基本分组结构未知的情况下确定重要的预测性聚类。其次，对于已知的分组结构，该项目开发了惩罚技术来执行分组选择，同时附加地允许实施分层约束。该项目的第三个组成部分是开发一种技术，在因素选择过程中采用方差分析进行典型的配对比较后分析。所有这三个组成部分都是在惩罚框架内通过对惩罚的适当选择来制定的。随着所有科学领域现有的丰富信息，决定大量可能的特征或变量中的哪些是重要的可能是一项压倒性的任务。因此，开发执行变量选择的技术是至关重要的。通常的情况是，科学家也想要发现一个潜在的群体结构。一个常见的例子出现在基因表达研究中，其中根据患者的基因表达谱将患者分类为疾病亚型是一个主要焦点。在基因表达研究的数千个基因中，只有一小部分实际上是疾病状态的有用指标，而且许多基因可以组合成功能基团。研究人员的研究特别着眼于实现这些类型的多方面分析，例如在找到相关基因的同时识别群体结构。这项研究的一个总主题是，适当设计的统计程序可以同时以综合方式实现多个目标。变量选择问题在所有学科中的重要性，以及研究人员与医学研究人员和其他科学家的合作，使得结果可以很容易地传播到应用研究社区，在那里它可以用来改善生活质量。

This project develops variable selection procedures in the context of grouped predictors, where the grouping structure can be either known or unknown. Known grouping structures include the case of Analysis of Variance (ANOVA) models where multiple `dummy' variables represent a single factor, or in nonparametric regression using basis functions. In these situations, it is desired to either include or exclude the entire set of variables as a group. Unknown grouping structure occurs when there are underlying clusters of predictors that have a combined effect on the response, such as a set of genes sharing a common pathway. This research addresses the issue of variable selection under both known and unknown grouping structures, while simultaneously addressing additional goals specific to the problem at hand. The first component of this project is combining `supervised clustering' and variable selection into a single step to facilitate the identification of important predictive clusters when the underlying grouping structure is unknown. Secondly, for the known grouping structure, this project develops penalization techniques to perform the grouped selection while additionally allowing for the enforcement of hierarchical constraints. The third component of the project is the development of a technique to perform the typical pairwise comparison post-hoc analysis in ANOVA within the factor selection process. All three components are developed in a penalization framework by appropriate choices of the penalty.With the abundance of information now available in all scientific fields, it can be an overwhelming task to decide on which of the massive number of possible characteristics, or variables, are important. Therefore, it is essential to develop techniques to perform variable selection. It is often the case that there is an underlying group structure that the scientist would like to discover as well. One common example occurs in gene expression studies, in which classification of patients into disease subtypes based on their gene expression profile is a major focus. Among the thousands of genes in a gene expression study, there is only a small fraction of them that are actually useful indicators of disease status, and many of the genes can be combined into functional groups. The investigator's research is particularly geared toward enabling the accomplishment of these types of multi-faceted analyses, such as finding the relevant genes while also identifying the group structure. A general theme of the research is that appropriately designed statistical procedures can achieve multiple objectives simultaneously and in an integrated fashion. The importance of the variable selection problem across all disciplines, and the investigator's collaborations with medical researchers and other scientists allows the results to be readily disseminated into the applied research community where it can be used to improve the quality of life.