Graphical Markov Models with Interpretable Structure

[j][2008]多元统计最核心的思想之一是对一组随机变量之间的依赖关系进行建模。这种分析的目的通常是试图对产生数据的过程提供一些见解。图形马尔可夫模型（GMMs）使用图形以简洁和计算效率高的方式表示多元统计依赖关系。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，通常不知道是否已经测量了所有相关变量，或者是否存在未测量的“混杂”变量。由于DAG模型的类别在边缘化下不是封闭的，如果观察到数据生成DAG中涉及的变量的子集，那么观察到的边缘的结果统计模型不一定对应于DAG。该项目将开发图形马尔可夫模型，该模型可以表示DAG模型对观察到的边缘施加的条件独立关系。这涉及到通过一组条件独立约束隐式描述的参数化分布；开发评估这些模型的技术，并为执行模型选择制定可计算的算法。在其众多应用中，gmm已在统计科学中变得普遍，用于分析列联表中的分类数据，用于模拟依赖空间的过程，例如流行病在人类和动物种群中的传播，以及用于开发恶劣天气条件的早期预警系统。它们在计算机科学（如贝叶斯网络）中用于信息处理和检索，用于机器人，计算机视觉和模式识别，用于复杂程序的调试（如Windows 95），以及用于医学诊断的专家系统的表示。在决策科学中（如影响图），作为信息流和控制的模型，并将许多决策者的意见结合起来。类似的模型在遗传学、社会学、计量经济学和周期计量学等领域早已被广泛使用。所有这些模型的一个关键特征是，它们代表了因果依赖关系的复杂网络。此外，这些模型允许快速计算实现。这些特性直接导致了它们在能够“推理”现实世界问题的软件开发中的核心作用。

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.