Collaborative Research: Integral Transform Methods for Sufficient Dimension Reduction in Regression

合作研究：回归中充分降维的积分变换方法

• 批准号: 0707004
• 负责人: Yu Michael Zhu
• 金额: $ 7.99万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0707004&HistoricalAwards=false
• 关键词: Collaborative; Research; Integral; Transform; Methods

This project is aimed to develop theory and methods for sufficient dimension reduction in regression analysis involving a large number of predictor variables. The investigators propose a general approach called the integral transform approach to facilitating dimension reduction. The key idea of this approach is to use integral transform and response transformation to change the domain where dimension reduction is performed. Due to the availability of a wide range of transformations and integral transforms, this approach leads to a flexible and effective framework for addressing and resolving challenges raised by high dimensionality. Through a series of well-defined research problems, the investigators study this framework and develop specific dimension reduction methods for many important regression applications. The success of this project not only provides effective practical tools for high-dimensional data analysis but also represents an advance in the theory and methodology of semiparametric inference.High-dimensional data that involve a large amount of variables are nowadays routinely generated and collected in areas such as scientific research, government, business, etc. It is well-known that high dimensionality causes difficulties in processing and analyzing these data. This is commonly referred to as the curse of dimensionality. There is an urgent demand of statistical tools that are able to mitigate the curse of dimensionality through dimension reduction. This project represents an answer to this demand and is particularly aimed at achieving dimension reduction in regression. The results from this project can be widely applied in areas where regression involving a large number of variables is required. Gene expression and protein sequence data analysis is one such example. Therefore, this project can help enhance scientific research and discovery and benefit a variety of social and economical activities.

该项目旨在开发涉及大量预测变量的回归分析中充分降维的理论和方法。研究人员提出了一种称为积分变换方法的通用方法来促进降维。该方法的关键思想是使用积分变换和响应变换来改变执行降维的域。由于广泛的变换和积分变换的可用性，这种方法产生了一个灵活有效的框架，用于应对和解决高维带来的挑战。通过一系列明确的研究问题，研究人员研究了这个框架，并为许多重要的回归应用开发了特定的降维方法。该项目的成功不仅为高维数据分析提供了有效的实用工具，而且代表了半参数推理理论和方法的进步。当今科学研究、政府、商业等领域经常生成和收集涉及大量变量的高维数据。众所周知，高维数据给处理和分析这些数据带来了困难。这通常被称为维数灾难。迫切需要能够通过降维来减轻维数灾难的统计工具。该项目代表了对这一需求的回答，特别旨在实现回归的降维。该项目的结果可广泛应用于需要进行大量变量回归的领域。基因表达和蛋白质序列数据分析就是这样的例子。因此，该项目有助于加强科学研究和发现，惠及各种社会和经济活动。