MATRIX REPRESENTATIONS AND INDEPENDENCIES IN DIRECTED ACYCLIC GRAPHS

• 成果类型: Article
• 署名作者: Marchetti, Giovanni M.; Wermuth, Nanny
• 署名单位: University of Florence; Chalmers University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS594
• 发表日期: 2009
• 页码: 961-978
• 关键词: systems

摘要

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.