Reading Dependencies from Covariance Graphs
2013 (English)In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 54, no 1, 216-227 p.Article in journal (Refereed) Published
The covariancegraph (aka bi-directed graph) of a probability distribution p is the undirected graphG where two nodes are adjacent iff their corresponding random variables are marginally dependent in p. (It is worth mentioning that our definition of covariancegraph is somewhat non-standard. The standard definition states that the lack of an edge between two nodes of G implies that their corresponding random variables are marginally independent in p. This difference in the definition is important in this paper.) In this paper, we present a graphical criterion for readingdependencies from G, under the assumption that p satisfies the graphoid properties as well as weak transitivity and composition. We prove that the graphical criterion is sound and complete in certain sense. We argue that our assumptions are not too restrictive. For instance, all the regular Gaussian probability distributions satisfy them.
Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 54, no 1, 216-227 p.
Chain graphs; Concentration graphs; Covariancegraphs
IdentifiersURN: urn:nbn:se:liu:diva-80298DOI: 10.1016/j.ijar.2012.06.025ISI: 000312520800012OAI: oai:DiVA.org:liu-80298DiVA: diva2:546463