Dimension Reduction Through Index Models

通过索引模型降维

• 批准号: 1209057
• 负责人: Peter Radchenko
• 金额: $ 12.96万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1209057&HistoricalAwards=false
• 关键词: Dimension; Reduction; Through; Index; Models

Historically statistics has dealt with extracting as much information as possible from a small data set. However, much of modern statistical research focusses on data sets that have enormous numbers of predictors. This phenomenon is a direct result of recent technological advances that have affected various fields of research, such as image processing, computational biology, and finance. This proposal addresses a very important question of fitting nonlinear regression models in high-dimensional situations, where the number predictors may be much larger than the number of observations. Unlike linear or generalized linear models, high-dimensional nonlinear regression is a very young research area that requires systematic and extensive development. Due to the curse of dimensionality, most of the work in this area has been conducted under the assumption that the regression function has a simple additive structure. The investigator proposes novel methodology for fitting index type regression models in high dimensions. The new methods cover models that are either complimentary or strictly more general than the additive models studied before. For each of the methods the proposal presents a computationally efficient fitting algorithm and lays out a plan for establishing theoretical results.The proposed research is expected to have a broad impact on the practice and education of statistics and related fields. Disciplines such as Computational Biology, Finance, Marketing and Machine Learning are highly interested in the type of methodology that is targeted in this proposal. The investigator plans to systematically develop software for implementing the proposed methods through free software packages and then make them readily available to researchers in the aforementioned fields. The proposed research will also have an impact on the growth and development of the new USC Statistics Ph.D. program. Several students in this young program will be involved in methodology research, algorithm development, and theoretical investigation. They will get hands on experience and guidance in the very important field of high-dimensional statistical inference.

从历史上看，统计学处理的是从一个小数据集中提取尽可能多的信息。然而，许多现代统计研究都集中在具有大量预测因子的数据集上。 这种现象是最近技术进步的直接结果，这些技术进步影响了各个研究领域，如图像处理，计算生物学和金融。 该建议解决了一个非常重要的问题，即在高维情况下拟合非线性回归模型，其中预测因子的数量可能远远大于观测值的数量。 与线性或广义线性模型不同，高维非线性回归是一个非常年轻的研究领域，需要系统和广泛的发展。 由于维数灾难，这一领域的大部分工作都是在假设回归函数具有简单的加性结构的情况下进行的。 研究者提出了一种新的方法来拟合高维指数型回归模型。 新的方法涵盖的模型，无论是互补的或严格更一般的添加剂模型研究之前。 对于每一种方法，该提案提出了一个计算效率高的拟合算法，并制定了建立理论结果的计划，预计拟议的研究将对统计和相关领域的实践和教育产生广泛的影响。 计算生物学、金融、市场营销和机器学习等学科对本提案中针对的方法论类型非常感兴趣。 研究人员计划通过免费软件包系统地开发用于实施拟议方法的软件，然后将其提供给上述领域的研究人员。 拟议的研究也将对新的USC统计博士的增长和发展产生影响。程序. 在这个年轻的程序的几个学生将参与方法研究，算法开发和理论研究。 他们将在高维统计推断这一非常重要的领域获得经验和指导。