Information Geometry with Application to Model Selection

信息几何在模型选择中的应用

• 批准号: 0631541
• 负责人: Jun Zhang
• 金额: $ 25万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-12-01 至 2012-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0631541&HistoricalAwards=false
• 关键词: Information; Geometry; Application; Model; Selection

Information Geometry with Application to Model SelectionAbstract of Proposed ResearchJun Zhang, Ovidiu Calin and Hiroshi MatsuzoeThis research is to further develop the mathematical foundations of information geometry and to apply it to the problem of model selection in social and behavioral science. Information geometry is a differential geometric approach to statistics in which models are represented as a set of points forming a manifold with properties invariant against specific parametrizations. We are particularly interested in investigating the use of the volume element of a manifold as a measure of model complexity.The core of many problems in the social and behavioral sciences often centers on making good selections between competing quantitative models. This project will investigate the use of various geometrical ideas for criteria of model selection.

信息几何及其在模型选择中的应用本研究旨在进一步发展信息几何的数学基础，并将其应用于社会和行为科学中的模型选择问题。信息几何是统计学的微分几何方法，其中模型被表示为形成流形的一组点，这些点具有针对特定参数化不变的属性。 我们特别感兴趣的是研究使用流形的体积元素作为模型复杂性的度量。在社会和行为科学中，许多问题的核心往往集中在相互竞争的定量模型之间做出良好的选择。本专题将探讨各种几何概念在模型选择标准中的应用。