Causal inference via graphical Markov models

NSERC发现基金支持的研究重点是模型选择。模型搜索是统计分析的重要组成部分，特别是在缺乏背景知识的情况下。本研究的主要目的是为某些变量可能未被观察到的过程开发一种有效的模型搜索程序。图形马尔可夫模型已被用于表示不同领域的过程，如经济学、社会科学、计算机科学和工程学。在这些设置中，通常假设过程可以用有向无环图（DAG）表示，其中相关变量形成图的顶点，顶点之间的箭头的存在或不存在编码变量之间的关系。在许多应用中，假设图的结构是已知的。最近，图形模型被用于从基因表达数据推断生物相互作用。在这种情况下，图的底层结构是未知的，可能有许多因果解释（图）是等效的，因为它们同样与观察到的数据一致。最近取得的进展是将这些解释的共同方面表示为一种表示，称为等效类。如果只有一些相关变量的数据可用，那么确定观察到的变量之间的每个因果解释如何在潜在（未观察到的）变量的存在下变化是有意义的。这项资助的工作旨在开发一种程序，该程序可以搜索具有潜在变量和选择变量的DAG模型的等效类。

The research supported by this NSERC Discovery grant focuses on model selection.  Model search is an important part of statistical analyses, particularly in the absence of background knowledge. The main objective of this research is to develop an efficient model search procedure for processes for which some variables may be unobserved. Graphical Markov models have been used to represent processes from diverse fields such as economics, social sciences, computer science, and engineering. In these settings it is often assumed that the process can be represented by a directed acyclic graph (DAG) in which the relevant variables form the vertices of the graph and the presence or absence of arrows between vertices encode the relationships between the variables.  In many applications, the structure of the graph is assumed known.   More recently, graphical models have been used to infer biological interactions from gene expression data. In such settings, where the underlying structure of the graph is unkown, there may be many causal explanations (graphs) that are equivalent in that they are equally consistent with observed data. Recent advances have been made to represent the common aspects of these explanations into one representation, called an equivalence class.   If data is available for only some of the relevant variables, then it is of interest to determine how every causal explanation among the observed variables change in the presence of latent (unobserved) variables.  The work supported by this grant aims to develop a procedure that searches across equivalence classes of DAG models with latent and selection variables.