Testing for Commonality Among Graphs and Subgraphs

• Activity Number: 223
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Daniel Sussman*+
• Companies: Johns Hopkins University
• Keywords: graph ; motif ; testing

Abstract

Many contemporary theories of neural information processing suggest that the neocortex employs hierarchical algorithms composed of repeated instances of a limited set of computing primitives. The cortical column conjecture suggests that neurons are connected in a graph that exhibits motifs representing repeated processing modules. We consider theory and methods for interrogating the structure of the cortical microcircuits, believed to embody these primitives. We model a cortical graph as a hierarchical block model with induced subgraphs which are themselves independent stochastic block models. Our focus is testing and estimating the extent to which the subgraphs share common structures, which would indicate that they form repeated motifs. We also investigate the problem of identifying candidate subgraphs and the impact of imperfect subgraph identification on subsequent inference. We demonstrate the efficacy of our preliminary investigation via bio-inspired simulation.