Advances in Variable Selection with Grouped Predictors

这个项目在分组预测的背景下开发变量选择程序，其中分组结构可以是已知的或未知的。已知的分组结构包括方差分析（ANOVA）模型的情况，其中多个"虚拟"变量表示单个因子，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。当存在对反应具有组合效应的潜在预测因子簇时，例如共享共同途径的一组基因，就会出现未知的分组结构。本研究解决了已知和未知分组结构下的变量选择问题，同时解决了当前问题特定的其他目标。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，以便在基本分组结构未知的情况下确定重要的预测聚类。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，同时还允许实施分层约束。该项目的第三个组成部分是开发一种技术，用于在因素选择过程中进行ANOVA中的典型成对比较事后分析。所有这三个组成部分都是在一个惩罚框架中通过适当的惩罚选择而发展起来的。随着现在所有科学领域都可以获得丰富的信息，在大量可能的特征或变量中确定哪些是重要的可能是一项压倒性的任务。因此，必须开发技术来执行变量选择。通常情况下，科学家也希望发现一个潜在的群体结构。一个常见的例子发生在基因表达研究中，其中基于其基因表达谱将患者分类为疾病亚型是一个主要焦点。在基因表达研究中的数千个基因中，只有一小部分是真正有用的疾病状态指标，许多基因可以组合成功能组。研究人员的研究特别适合于实现这些类型的多方面分析，例如找到相关基因，同时确定群体结构。研究的一个总的主题是，适当设计的统计程序可以同时实现多个目标，并以综合的方式。变量选择问题在所有学科中的重要性，以及研究者与医学研究人员和其他科学家的合作，使得研究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.