Node Classification in Networks of Stochastic Evidence Accumulators

This paper considers a network of stochastic evidence accumulators, each represented by a driftdiffusion model accruing evidence towards a decision in continuous time by observing a noisy signal and by exchanging information with other units according to a fixed communication graph. We bring into focus the relationship between the location of each unit in the communication graph and its certainty as measured by the inverse of the variance of its state. We show that node classification according to degree distributions or geodesic distances cannot faithfully capture node ranking in terms of certainty. Instead, all possible paths connecting each unit with the rest in the network must be incorporated. We make this precise by proving that node classification according to information centrality provides a rank ordering with respect to node certainty, thereby affording a direct interpretation of the certainty level of each unit in terms of the structural properties of the underlying communication graph. Index Terms Drift diffusion, networks, communication graphs, evidence accumulation, decision making, centrality. Manuscript submitted on October 16, 2012. Preliminary parts of this paper appear in [1], [2]. I. Poulakakis is with the Department of Mechanical Engineering, University of Delaware, Newark, DE 19711, USA; e-mail: [email protected]. L. Scardovi is with the Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, M5S 3G4, Canada; e-mail: [email protected]. N. E. Leonard is with the Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA; e-mail: [email protected]. May 3, 2014 DRAFT I. POULAKAKIS, L. SCARDOVI, N. E. LEONARD 2