Graph-Theoretic Distributed Inference in Social Networks

Abstract

We consider distributed inference in social networks where a phenomenon of interest evolves over a given social interaction graph, referred to as the social digraph. For inference, we assume that a network of agents monitors certain nodes in the social digraph and no agent may be able to perform inference within its neighborhood; the agents must rely on inter-agent communication. The key contributions of this paper include: (i) a novel construction of the distributed estimator and distributed observability from the first principles; (ii) a graph-theoretic agent classification that establishes the importance and role of each agent towards inference; (iii) characterizing the necessary conditions, based on the classification in (ii), on the agent network to achieve distributed observability. Our results are based on structured systems theory and are applicable to any parameter choice of the underlying system matrix as long as the social digraph remains fixed. In other words, any social phenomena that evolves (linearly) over a structure-invariant social digraph may be considered-we refer to such systems as Liner Structure-Invariant (LSI). The aforementioned contributions, (i)-(iii), thus, only require the knowledge of the social digraph (topology) and are independent of the social phenomena. We show the applicability of the results to several real-wold social networks, i.e. social influence among monks, networks of political blogs and books, and a co-authorship graph.

Single-Bit Consensus With Finite-Time Convergence: Theory and Applications

“…In the above formulation, A is the dynamical system matrix, k is the time-step, y k i is the measurement of agent i at time-step k, and v k and r k i are the noise terms. Following the distributed estimation protocol in [10], [35]- [38], the following protocol based on the consensus-update law (3) is considered:…”

Minimal Sufficient Conditions for Structural Observability/Controllability of Composite Networks via Kronecker Product

“…Proof: The proof is given in our previous work [23], [52] for observability. In fact, for any choice of maximum matching, there is one unmatched node in every dilation and similar statement holds for contractions.…”

“…where q k collects the noise terms, e i k = x k|k − x i k|k is the estimation error at agent i, e k is the global estimation error and D H represents the global measurement matrix associated with distributed estimation. It is well known that the error dynamics (11) are bounded if the pair (W ⊗ A, D H ) is observable, also known as distributed observability [23], [26]. The distributed observability, in fact, refers to the observability of the composite network G 1 × G 2 , where G 1 and G 2 are respectively associated to matrices sensor communication W and the system matrix A.…”

“…In this paper, we discuss the structural controllability and observability of the composite networks representing dynamical systems. We assume the underlying dynamical system to be LSI which is prevalent, among others, in social networks [23], [29]- [31]. In LSI systems, the system structure (representing the network) is fixed while the system parameters (and consequently the link weights in the network) may vary over time.…”

Minimal Driver Nodes for Structural Controllability of Large-Scale Dynamical Systems: Node Classification

“…systems [7]- [9]. Due to the large size of these systems, the identification of a small fraction of their states to drive the entire system around the state space poses an important problem.…”