Graphical Markov Models with Interpretable Structure

具有可解释结构的图形马尔可夫模型

• 批准号: 9972008
• 负责人: Thomas Richardson
• 金额: $ 15.5万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-12-15 至 2003-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9972008&HistoricalAwards=false
• 关键词: Graphical; Markov; Models; Interpretable; Structure

9972008One of the most central ideas of multivariate statistics is the modeling of dependencies among a set of stochastic variables. The aim of such an analysis is often to try to provide some insight into the process which generated the data. Graphical Markov models (GMMs) use graphs to represent multivariate statistical dependencies in a parsimonious and computationally efficient manner. Directed acyclic graphs (DAGs) also provide a natural formalism for representing data generation mechanisms. In the case of observational data it is often not known whether all of the relevant variables have been measured, or whether unmeasured 'confounding' variables are present. Since the class of DAG models is not closed under marginalization, if a subset of the variables involved in a data generating DAG are observed, then the resulting statistical model for the observed margin will not necessarily correspond to a DAG. This project will develop graphical Markov models that can represent the conditional independence relations imposed by a DAG model on an observed marginal. This involves parametrizing distributions described implicitly via a set of conditional independence constraints; developing techniques for estimating these models, and formulating computationally tractable algorithms for performing model selection.Among their many applications, GMMs have become prevalent in statistical science for the analysis of categorical data in contingency tables, for the modeling of spatially-dependent processes such as the spread of epidemics in human and animal populations, and for the development of early warning systems for severe weather conditions. They are used in computer science (as Bayesian networks) for information processing and retrieval, for robotics, computer vision, and pattern recognition, for the debugging of complex programs (such as Windows 95), and for the representation of expert systems for medical diagnosis. In decision science (as influenced diagrams) as models for information flow and control and for combining the opinions of many decision-makers. Similar models have long been used infield such as genetics, sociology, econometrics, and cycle metrics. A crucial feature of all these models is that they represent complex networks of causal dependencies. In addition, these models allow for fast computational implementation. These features have led directly to their central role in the development of software that can "reason" about real world problems.

9972008多元统计学最核心的思想之一是对一组随机变量之间的相关性进行建模。这种分析的目的通常是试图对产生数据的过程提供一些洞察。图形马尔可夫模型(GMM)使用图来表示多变量统计相关性，以一种简洁且计算高效的方式。有向无环图(DAG)也为表示数据生成机制提供了一种自然的形式。在观测数据的情况下，通常不知道是否所有相关变量都已被测量，或者是否存在未测量的“混杂”变量。由于DAG模型的类在边际化下不是封闭的，如果观察到在生成DAG的数据中涉及的变量的子集，则所得到的用于所观察的边际的统计模型将不一定对应于DAG。这个项目将开发图形马尔可夫模型，它可以表示DAG模型在观察到的边际上强加的条件独立关系。这包括通过一组条件独立性约束对隐含描述的分布进行参数化；开发估计这些模型的技术，并制定执行模型选择的易于计算的算法。在它们的许多应用中，GMM在统计科学中已变得普遍，用于分析列联表中的分类数据，用于对空间相关过程(如流行病在人类和动物种群中的传播)的建模，以及用于开发恶劣天气条件的早期预警系统。它们被用于计算机科学中(作为贝叶斯网络)用于信息处理和检索、用于机器人学、计算机视觉和模式识别、用于复杂程序的调试(例如Windows 95)以及用于表示用于医疗诊断的专家系统。在决策科学中(如受影响的图表)，作为信息流和控制的模型，并结合许多决策者的意见。类似的模型早已在遗传学、社会学、计量经济学和周期计量学等领域得到应用。所有这些模型的一个关键特征是，它们代表了因果依赖的复杂网络。此外，这些模型允许快速的计算实现。这些功能直接导致了它们在软件开发中的核心作用，这些软件可以对现实世界的问题进行“推理”。