Collaborative Research: Graphical and Algebraic Models for Multivariate Categorical Data

协作研究：多元分类数据的图形和代数模型

• 批准号: 0505612
• 负责人: Mathias Drton
• 金额: --
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505612&HistoricalAwards=false
• 关键词: Collaborative; Research; Graphical; Algebraic; Models

The proposed research project develops models for multivariate categoricaldata by mimicking Gaussian models with a desired model structure that canbe captured in terms of the non-parametric concept of conditionalindependence. This method has a long history: graphical log-linear modelscan be induced in this way by Gaussian models defined by zero constraintson the inverse covariance matrix. The project seeks to greatly extend thescope of the approach. It is proposed to define and study marginalindependence models for contingency tables, discrete-valued time serieswith moving average-like dependence structure, seemingly unrelatedregressions with discrete response variables, and discrete graphicalmodels based on the recently introduced AMP chain graphs and ancestralgraphs. The main objectives of the study are development ofparameterizations, construction and implementation of efficient algorithmsfor maximum likelihood estimation, and investigation of procedures formodel selection. A particular focus of the project will be on employingmodern tools from computational algebra in the analysis of the structure ofparameter spaces and properties of likelihood functions.Multivariate statistical models seek to describe the complex relationshipsbetween a large set of variables. A particular class of such models,called graphical models, has found wide-spread application in fields likeartificial intelligence, bio-informatics, biology, epidemiology, andspeech recognition. The models proposed in the project extend the realmof graphical models and it is anticipated that they will be applied inmany of these fields. Moreover, the proposed methodology will provide newtools for the analysis of data of public interest such as census data.The researchers also plan to make software tools freely available as partof a larger open source statistical software package called R.

拟议的研究项目开发模型的多变量categoricaldata通过模仿高斯模型与所需的模型结构，可以捕获的条件独立的非参数概念。 这种方法有很长的历史：图形对数线性模型可以用这种方法由逆协方差矩阵上零约束定义的高斯模型导出。该项目旨在大大扩展该方法的范围。 基于最近引入的AMP链图和祖先图，提出了定义和研究列联表、具有移动平均相关结构的离散值时间序列、具有离散响应变量的似不相关回归以及离散图模型的边际独立模型。 研究的主要目标是参数化的发展，最大似然估计的有效算法的建设和实施，以及模型选择的程序调查。该项目的一个特别重点将是在分析参数空间的结构和似然函数的性质时使用计算代数的现代工具。多变量统计模型试图描述大量变量之间的复杂关系。一类特殊的模型，称为图形模型，在人工智能、生物信息学、生物学、流行病学和语音识别等领域有着广泛的应用。 该项目中提出的模型扩展了图形模型的领域，预计它们将在许多领域中得到应用。 此外，所提出的方法将为分析人口普查数据等公众感兴趣的数据提供新的工具。研究人员还计划将软件工具作为一个更大的开源统计软件包R的一部分免费提供。