Bayesian methods for structure detection in analysis of object data

对象数据分析中的结构检测贝叶斯方法

• 批准号: 1106570
• 负责人: Subhashis Ghoshal
• 金额: $ 25万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-01 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106570&HistoricalAwards=false
• 关键词: Bayesian; methods; structure; detection; analysis

Complex data objects such as images, functional data, random sets, shapes, graphs and trees are nowadays commonly used to represent information present in observations. Bayesian methods are well suited for detecting meaningful structures hidden underneath these complex data sets. The structure may come in the form of sparsity, setting many parameter values to a null value like zero, or by making adjacent values equal, thus effectively reducing the number of parameters to handle. This project will provide definitive guidelines for constructing prior distributions on the parameters controlling the distributions of object data, and for computing the resulting posterior distributions in an efficient manner. The main idea of the research is to use an auxiliary stochastic process to control ties in object data. The project connects diverse concepts such as multi-scale modeling, feature sharing, multiple testing, random geometry, machine learning and nonparametric Bayesian paradigm, and synthesizes these different concepts into a powerful approach for analyzing object data. The project also stimulates the development of computing strategies that exploit structural niceties such as conditional conjugacy, thus providing fast and accurate computational approaches.This project develops methodologies that will provide a foundation for finding structures in collections of data, with a wide range of applications in astronomy, medical sciences, engineering, finance, and various other fields. The research will help process astronomical images in a more accurate and efficient manner, and thus help identify events in distant supernova remnants and other astronomical bodies. The research will also have a significant impact in medical imaging, by providing a method of accurate processing of scans of sensitive organs with very little exposure to harmful rays. The project will impact human resource development in the form of graduate student advising. The project will have subprojects that will be suitable topics for undergraduate research projects. Efforts will be made to involve students from under-represented groups to promote diversity.

复杂的数据对象，如图像、功能数据、随机集、形状、图形和树，现在通常用于表示观测中存在的信息。贝叶斯方法非常适合于检测隐藏在这些复杂数据集下面的有意义的结构。这种结构可能以稀疏性的形式出现，将许多参数值设置为零之类的空值，或者使相邻的值相等，从而有效地减少要处理的参数数量。该项目将为在控制对象数据分布的参数上构建先验分布以及以有效的方式计算产生的后验分布提供明确的指导方针。该研究的主要思想是利用一个辅助的随机过程来控制对象数据中的联系。该项目将多尺度建模、特征共享、多重测试、随机几何、机器学习和非参数贝叶斯范式等不同的概念联系起来，并将这些不同的概念综合成一种分析对象数据的强大方法。该项目还刺激了利用结构细节（如条件共轭）的计算策略的发展，从而提供了快速和准确的计算方法。该项目开发的方法将为在数据集合中发现结构提供基础，在天文学、医学、工程、金融和各种其他领域具有广泛的应用。这项研究将有助于以更准确、更有效的方式处理天文图像，从而有助于识别遥远的超新星遗迹和其他天体中的事件。这项研究还将对医学成像产生重大影响，因为它提供了一种精确处理敏感器官扫描的方法，同时很少暴露在有害射线中。该项目将以研究生指导的形式影响人力资源开发。该项目将有子项目，这些子项目将适合本科生研究项目的主题。将努力让来自代表性不足群体的学生参与进来，以促进多样性。