New Statistical Modeling Procedures for Object Oriented Data Analysis (OODA)

面向对象数据分析 (OODA) 的新统计建模程序

• 批准号: 0706761
• 负责人: Haonan Wang
• 金额: $ 14.99万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-01 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706761&HistoricalAwards=false
• 关键词: New; Statistical; Modeling; Procedures; Object

The objectives of this research are to develop novel statistical models, theory, algorithms and applications geared towards the analysis of complex object oriented data, including tree-structured objects and random graphs. The research not only introduces a number of innovative techniques, but also provides various new and deep insights into statistical foundations, e.g., modeling procedure for complex data objects. This research significantly enhances the toolkit available for the analysis of object oriented data. In particular, three inter-related topics are proposed for investigation. First, the investigator develops a careful axiomatic structure for understanding tree-structured objects, which circumvents the need to define linear operations. Moreover, the investigator studies how to carry out statistical inference, based on the metric induced probability measures, in tree space. Nonparametric and semiparametric modeling procedures are also proposed in the space of trees and graphs. Second, a model selection procedure is studied using Hellinger distance. The asymptotic behavior of the estimated Hellinger discrepancy, and testing the adequacy of the approximation are considered. The performance of the proposed model selection procedure is examined through its application to the microarray gene expression data. Third, the investigator develops new techniques for analyzing data collected on manifolds. Manifold data, such as data collected along a river in an ecological study, and data gathered over a surface, have become popular in many scientific fields. New statistical methodology to extract useful features from manifold data is needed. Here, a geodesic low-rank thin plate splines method is under investigation.The research project lays out a well-grounded and comprehensive framework for analysis of object oriented data. It greatly enhances the research on object oriented data analysis by developing interdisciplinary research including bioinformatics, computer science, neuroscience, mathematics and statistics. The research on tree-structured objects can significantly benefit society by developing new techniques in image analysis and improving medical diagnoses. The investigator integrates research and education by working closely with both undergraduate and graduate students, especially underrepresented groups, from various fields. In addition, the results are to be disseminated through presentations, tutorials and conferences and via internet.

本研究的目标是开发新的统计模型、理论、算法和应用程序，以分析复杂的面向对象的数据，包括树状结构的对象和随机图。该研究不仅引入了许多创新技术，而且为统计基础提供了各种新的和深刻的见解，例如复杂数据对象的建模过程。这项研究显著增强了用于分析面向对象数据的工具包。特别提出了三个相互关联的主题进行研究。首先，研究者为理解树状结构的对象开发了一个谨慎的公理结构，这规避了定义线性操作的需要。此外，研究者还研究了如何在树空间中基于度量诱导概率测度进行统计推断。在树和图的空间中提出了非参数和半参数的建模方法。其次，研究了基于海灵格距离的模型选择过程。考虑了估计的Hellinger差异的渐近性，并检验了近似的充分性。所提出的模型选择程序的性能通过其应用于微阵列基因表达数据进行了检验。第三，研究者开发了新的技术来分析在流形上收集的数据。多种数据，如在生态研究中沿着河流收集的数据，以及在地表收集的数据，在许多科学领域都很受欢迎。需要新的统计方法从流形数据中提取有用的特征。本文研究了一种测地线低阶薄板样条法。该研究项目为分析面向对象的数据提供了一个基础良好且全面的框架。它通过发展生物信息学、计算机科学、神经科学、数学和统计学等跨学科研究，极大地促进了面向对象数据分析的研究。对树状结构物体的研究可以通过开发图像分析新技术和改进医学诊断来显著地造福社会。研究者通过与来自不同领域的本科生和研究生，特别是代表性不足的群体密切合作，将研究和教育结合起来。此外，研究结果将通过演讲、教程和会议以及互联网传播。