Flexible Modeling for High-Dimensional Complex Data: Theory, Methodology, and Computation

高维复杂数据的灵活建模：理论、方法和计算

• 批准号: 1309507
• 负责人: Hao Zhang
• 金额: $ 15万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1309507&HistoricalAwards=false
• 关键词: Flexible; Modeling; Dimensional; Complex; Data

In high dimensional data analysis, the relationships among predictors can be highly nonlinear and non-additive, and taking into account such complex structures may significantly improve model prediction power and provide crucial insight about the underlying data generation mechanism. The goal of this project is to develop and study new statistical and data mining methodologies for detecting nonlinear and non-additive patterns in high dimensional sparse models. When the data dimension is ultra-high, interaction selection is extremely challenging, both numerically and theoretically, due to curse of dimensionality. There are very limited tools available in practice and theory is scant. In this project, the investigators give a comprehensive treatment to the problem of high-dimensional interaction selection. They propose and study novel selection and modeling techniques for a variety of regression and classification models. Fast and robust large-scale computational algorithms are derived. In addition, the investigators are committed to establishing high dimensional theory for interaction selection and providing a solid foundation for the new methods. The investigators also propose and study a unified theory and computation framework to identify nonlinear effects for a broad class of nonparametric regression models. Special effort is spent on addressing computational issues such as multiple parameter tuning, regularization solution path/surface algorithms, and development of user friendly statistical software packages.Big and high dimensional data offer us fascinating and unprecedented opportunities to gain extraordinary insight from data. On the other hand, the scale and volume of data create tremendous challenges for standard analysis tools to extract useful information. The goal of this project is to develop innovative statistical and data mining methods, solid mathematical theory, and powerful computational tools and software to capture hidden and possibly complex patterns when the data dimension is high. One challenging problem to be tackled in this project is high dimensional interaction selection. In genome-wide association studies (GWAS), there is growing evidence that gene-gene and gene-environment interactions can provide key insight about complex biological pathways that underpin human diseases. However, there are very few effective, well-grounded, and computationally attractive tools available in practice to identify interactions for high dimensional data. The investigators try to fill this gap by conducting thorough investigation on the problem. The results from this project research can significantly advance theory and as well as contribute new statistical tools for practical use. The proposed methods have a wide range of scientific applications such as biology, biomedicine, and environmental studies. This project integrates research, education, and interdisciplinary collaboration through developing new graduate and undergraduate courses and involving students in the research activities.

在高维数据分析中，预测因子之间的关系可能是高度非线性和非添加的，并且考虑到这种复杂的结构可以显着提高模型预测能力，并提供有关基本数据生成机制的重要见解。该项目的目的是开发和研究用于检测高维稀疏模型中非线性和非添加模式的新统计和数据挖掘方法。当数据维度超高时，由于维度的诅咒，相互作用的选择在数值和理论上都是极具挑战性的。实践中有非常有限的工具，理论很少。在这个项目中，研究人员对高维相互作用选择的问题进行了全面处理。他们建议并研究各种回归和分类模型的新颖选择和建模技术。得出了快速，稳健的大规模计算算法。此外，研究人员致力于建立高维理论以进行相互作用选择，并为新方法提供坚实的基础。研究人员还提出并研究了一个统一的理论和计算框架，以确定一系列非参数回归模型的非线性效应。花在解决计算问题上花费了特殊的精力，例如多个参数调整，正则化解决方案路径/表面算法以及用户友好的统计软件包的开发。BIG和高维数据为我们提供了有趣且前所未有的机会，可以从数据中获得非凡的洞察力。另一方面，数据的规模和数量为标准分析工具提出有用信息带来了巨大的挑战。该项目的目的是开发创新的统计和数据挖掘方法，可靠的数学理论以及强大的计算工具和软件，以捕获数据维度较高时隐藏和可能的复杂模式。在这个项目中要解决的一个具有挑战性的问题是高维相互作用的选择。在全基因组关联研究（GWAS）中，越来越多的证据表明，基因基因和基因环境相互作用可以提供有关基于人类疾病的复杂生物学途径的关键见解。但是，实践中可用的有效，良好和计算上有吸引力的工具几乎没有可用于确定高维数据的相互作用的工具。研究人员试图通过对问题进行彻底调查来填补这一空白。该项目研究的结果可以大大提高理论，并为实践使用贡献新的统计工具。所提出的方法具有广泛的科学应用，例如生物学，生物医学和环境研究。该项目通过开发新的研究生和本科课程并让学生从事研究活动，将研究，教育和跨学科合作整合在一起。