UBC Theses and Dissertations

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UBC Theses and Dissertations

Statistical signal processing on dynamic graphs with applications in social networks Hamdi, Maziyar


Due to the proliferation of social networks and their significant effects on our day-to-day activities, there has been a growing interest in modeling and analyzing behavior of agents in social networks over the past decade. The unifying theme of this thesis is to develop a set of mathematical theories and algorithmic tools for different estimation and sensing problems over graphs with applications to social networks. The first part of this dissertation is devoted to multi-agent Bayesian estimation and learning problem in social networks. We consider a set of agents that interact over a network to estimate an unknown parameter called state of nature. As a result of the recursive nature of Bayesian models and the correlation introduced by the structure of the underlying communication graph, information collected by one agent can be mistakenly considered independent, that is, mis-information prop- agation, also known as data incest arises. This part presents data incest removal algorithms that ensure complete mitigation of the mis-information associated with the estimates of agents in two different information exchange patterns: First, a scenario where beliefs (posterior distribution of state of nature) are transmitted over the network. Second, a social learning context where agents map their local beliefs into a finite set of actions and broadcast their actions to other agents. We also present a necessary and sufficient condition on the structure of information flow graph to mitigate mis-information propagation. The second part of the thesis considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite state Markov chain. This part presents two results. First, motivated by social network applications, the asymptotic behavior of the degree distribution is analyzed. Second, a stochastic approximation algorithm is presented to track empirical degree distribution as it evolves over time. The tracking performance of the algorithm is analyzed in terms of mean square error and a functional central limit theorem is presented for the asymptotic tracking error.

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