On the Decomposition of Pairwise Association Measures Along the Paths of an Undirected Concentration Graph Model.

• Activity Number: 636 - Graphical Models: From Foundations to Applications
• Type: Invited
• Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Alberto Roverato* and Robert Castelo
• Companies: University of Padua and Universitat Pompeu Fabra
• Keywords: Concentration graph model; Covariance decomposition; Graphical model; Path weights

Abstract

In the analysis of graphical Gaussian models, Jones and West (Biometrika, 2005) associated a weight to every path in the network and showed that the covariance between two variables can be computed as the sum of the weights of all the paths joining the two variables. Such weights allow one to compare paths with common endpoints, and therefore, to identify the relative contribution of a path to the value of the corresponding covariance. However, it is not clear either how to interpret the value of a single path or how to compare two paths with different endpoints. Here, we provide a precise interpretation of the value of the weights obtained from the decomposition of a covariance, and then provide a general formulation of the theory to include, as special cases, other relevant measures of association such as correlations and inflated correlations. We identify a class of paths, called chordless paths, whose weights have a straightforward interpretation. All the paths in a tree are chordless and we show how, in this context, path weights can provide a new tool for differential networking analysis.