Constrained Group Selection and Structure Estimation in Semiparametric Models

本申请提出了一类新的约束组选择方法在高维模型的参数时，有自然的约束。预计该项目将激发新的研究方向，研究几个重要的统计建模和分析问题，其中包括半参数加性模型，变系数模型和生存分析模型中的结构估计和变量选择在高维设置的变量的数量大于样本容量。该项目还将为多个基因组数据集的综合分析和全基因组关联研究提供新的方法。所提出的方法在高维设置和计算算法的理论属性将被开发。高维数据的分析提出了新的和具有挑战性的统计理论和计算问题。假设变量数量固定且远小于样本大小的标准方法不适用于高维模型。所提出的方法预计能够正确地选择重要的群体，并正确地估计模型结构，在稀疏，高维设置的高概率。高维数据出现在许多不同的科学和人文领域，包括生物学，经济学，金融，信息技术和健康科学。在所有这些领域中，特征选择是从数据中发现知识的过程中的关键步骤。在基因和基因组研究方面，随着生物技术的迅速发展，正在产生越来越多的大数据集。从高维和噪声数据集中识别统计和生物学上有意义的模式正成为一个主要的挑战。在估计临床结果和遗传数据之间的关系时，可以处理高维问题的统计方法的发展将有助于更好地理解疾病的遗传基础，更好的诊断和更好的生存预测。该方法可应用于高维删失生存数据、纵向数据、全基因组关联研究（GWAS）和多基因组数据集的综合分析。删失和纵向数据出现在许多临床和生物医学研究中。GWAS和整合分析是鉴定常见和复杂疾病易感基因的重要方法。临床和遗传研究的最终目标是了解风险因素和表型之间的关系，以开发预防，诊断和治疗疾病的新方法。该项目旨在将新的统计方法转化为分析高维临床和基因组数据的新方法，这些数据对实现这一目标至关重要。从拟议的项目的方法和结果将被纳入研究生课程高维数据分析。研究人员将向科学期刊提交论文，并在互联网上公开发表论文和计算机程序，从而向科学界广泛传播研究结果。研究人员还将在科学会议和讲习班上介绍研究结果。

This application proposes a class of novel constrained group selection methods in high-dimensional models when there are natural constraints on the parameters. The proposed project is expected to stimulate new research directions for studying several important statistical modeling and analysis problems, which include structure estimation and variable selection in semiparametric additive models, varying coefficient models, and survival analysis models in high-dimensional settings where the number of variables is larger than the sample size. The proposed project will also yield new methods for integrative analysis of multiple genomic datasets and genome wide association studies. Theoretical properties of the proposed methods in high-dimensional settings and computational algorithms will be developed. Analysis of high-dimensional data presents new and challenging theoretical and computational questions in statistics. Standard methods assuming the number of variables is fixed and much smaller than the sample size are not applicable to high-dimensional models. The proposed methods are expected to be able to correctly select the important groups and correctly estimate model structures with high probability in sparse, high-dimensional settings. High-dimensional data arise in many diverse fields of sciences and humanities, including biology, economics, finance, information technology, and health sciences. In all these fields, feature selection is a crucial step in the process of knowledge discovery from data. In genetic and genomic research, with rapid advances in biotechnology, more and more big data sets are being generated. The identification of statistically and biologically significant patterns from high-dimensional and noisy data sets is becoming a major challenge. The development of statistical methods that can deal with high-dimensional problems in estimating the relationship between clinical outcomes and genetic data will contribute to better understanding of the genetic basis of diseases, better diagnoses, and better survival prediction. The proposed methods will be applied to the analysis of high-dimensional censored survival data, longitudinal data, genome wide association studies (GWAS) and integrative analysis of multiple genomic datasets. Censored and longitudinal data arise in many clinical and biomedical studies. GWAS and integrative analysis are important methods for identifying disease susceptibility genes for common and complex diseases. The ultimate goal of clinical and genetic research is to understand the relationships between risk factors and phenotypes for developing new approaches to prevention, diagnosis and treatment of disease. This project aims to translate novel statistical approaches into new methodologies for analyzing high-dimensional clinical and genomic data that are important in achieving this goal. The methods and results from the proposed project will be incorporated into a graduate course on high-dimensional data analysis. The investigator will broadly disseminate the results to the scientific community by submitting papers to scientific journals and making them and the computer programs publicly available on the internet. The investigator will also present the results in scientific conferences and workshops.