Statistical inference on attributed random graphs: Fusion of graph features and content

Many problems can be cast as statistical inference on an attributed random graph. Our motivation is change detection in communication graphs. We prove that tests based on a fusion of graph-derived and content-derived metadata can be more powerful than those based on graph or content features alone. For some basic attributed random graph models, we derive fusion tests from the likelihood ratio. We describe the regions in parameter space where the fusion improves power, using both numeric results from selected small examples and analytic results on asymptotically large graphs.