Variable Selection, Variable Screening and Dimension Reduction

该建议的目标是（1）通过合并变量选择和降维领域的想法来丰富变量选择方案，以及（2）使用联想学习的替代方法来开发变量筛选程序。具体目标包括：a）开发降维后的模型检验程序，B）使用模型检验程序和多重检验思想开发变量选择程序，c）使用矩阵正则化开发用于非常高维数据的降维程序，d）基于偏相关学习开发变量筛选，e）使用非参数关联学习开发变量筛选。包括基因表达和蛋白质组学研究，生物医学成像，功能性磁共振成像，断层扫描，肿瘤分类，信号处理，图像分析，金融，文本检索和气候研究，所收集的数据包括大量变量，其中只有少数变量与预测有关。确定相关预测因素的程序大多是在某些模型假设下制定的，可能无法识别某些重要预测因素的相关性。拟议的研究旨在开发变量筛选和变量选择程序，不依赖于潜在的限制性建模假设。

The objectives of this proposal are (1) to enrich the variable selection alternatives by merging ideas from the variable selection and dimension reduction areas, and (2) develop variable screening procedures using alternative methods of association learning. The specific goals include: a) develop post-dimension reduction model checking procedures, b) develop variable selection procedures using the model checking procedures and multiple testing ideas, c) develop dimension reduction procedures for very high dimensional data using matrix regularization, d) develop variable screening based on partial correlation learning, e) develop variable screening using nonparametric association learning.In many areas of contemporary research, including gene expression and proteomics studies, biomedical imaging, functional magnetic resonance imaging, tomography, tumor classifications, signal processing, image analysis, finance, text retrieval and climate studies, the data collected include a large number of variables with only a few of them being relevant for prediction. Procedures for identifying the relevant predictors have mostly been developed under certain model assumptions and may fail to discern the relevance of some important predictors. The proposed research aims at developing variable screening and variable selection procedures which do not rely on potentially restrictive modeling assumptions.