Dynamics of Social Networks: Multi-agent Information Fusion, Anticipatory Decision Making and Polling

This paper surveys mathematical models, structural results and algorithms in controlled sensing with social learning in social networks. Part 1, namely Bayesian Social Learning with Controlled Sensing addresses the following questions: How does risk averse behavior in social learning affect quickest change detection? How can information fusion be priced? How is the convergence rate of state estimation affected by social learning? The aim is to develop and extend structural results in stochastic control and Bayesian estimation to answer these questions. Such structural results yield fundamental bounds on the optimal performance, give insight into what parameters affect the optimal policies, and yield computationally efficient algorithms. Part 2, namely, Multi-agent Information Fusion with Behavioral Economics Constraints generalizes Part 1. The agents exhibit sophisticated decision making in a behavioral economics sense; namely the agents make anticipatory decisions (thus the decision strategies are time inconsistent and interpreted as subgame Bayesian Nash equilibria). Part 3, namely {\em Interactive Sensing in Large Networks}, addresses the following questions: How to track the degree distribution of an infinite random graph with dynamics (via a stochastic approximation on a Hilbert space)? How can the infected degree distribution of a Markov modulated power law network and its mean field dynamics be tracked via Bayesian filtering given incomplete information obtained by sampling the network? We also briefly discuss how the glass ceiling effect emerges in social networks. Part 4, namely \emph{Efficient Network Polling} deals with polling in large scale social networks. In such networks, only a fraction of nodes can be polled to determine their decisions. Which nodes should be polled to achieve a statistically accurate estimates

Using a Bayesian approach to reconstruct graph statistics after edge sampling

Often, due to prohibitively large size or to limits to data collecting APIs, it is not possible to work with a complete network dataset and sampling is required. A type of sampling which is consistent with Twitter API restrictions is uniform edge sampling. In this paper, we propose a methodology for the recovery of two fundamental network properties from an edge-sampled network: the degree distribution and the triangle count (we estimate the totals for the network and the counts associated with each edge). We use a Bayesian approach and show a range of methods for constructing a prior which does not require assumptions about the original network. Our approach is tested on two synthetic and three real datasets with diverse sizes, degree distributions, degree-degree correlations and triangle count distributions.Comment: Extended version of the paper accepted in Complex Networks 202