Tracking a Markov-Modulated Stationary Degree Distribution of a Dynamic Random Graph

Hamdi, Maziyar; Krishnamurthy, Vikram; Yin, Gang

doi:10.1109/tit.2014.2346183

Cited by 19 publications

(14 citation statements)

References 34 publications

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“…We briefly mention two more extensions. Hamdi, Krishnamurthy and Yin [11], also motivated by social networks, introduce a variant where the probabilities that a vertex is deleted and that when a duplication step takes place that the new vertex connects to each neighbour of its parent are dependent on the state of an underlying Markov chain. Finally, a model where the duplication probabilities are proportional to the degree instead of uniform is considered in Cohen, Jordan and Voliotis [10], but rigorous results are only obtained for the case of full duplication.…”

Section: Other Duplication Modelsmentioning

confidence: 99%

The connected component of the partial duplication graph

Jordan¹

2018

ALEA

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We consider the connected component of the partial duplication model for a random graph, a model which was introduced by Bhan, Galas and Dewey as a model for gene expression networks. The most rigorous results are due to Hermann and Pfaffelhuber, who show a phase transition between a subcritical case where in the limit almost all vertices are isolated and a supercritical case where the proportion of the vertices which are connected is bounded away from zero.We study the connected component in the subcritical case, and show that, when the duplication parameter p < e −1 , the degree distribution of the connected component has a limit, which we can describe in terms of the stationary distribution of a certain Markov chain and which follows an approximately power law tail, with the power law index predicted by Ispolatov, Krapivsky and Yuryev. Our methods involve analysing the quasi-stationary distribution of a certain continuous time Markov chain associated with the evolution of the graph.

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Section: Other Duplication Modelsmentioning

confidence: 99%

The connected component of the partial duplication graph

Jordan¹

2018

ALEA

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“…We refer the reader to [108] for details and also posterior Cramer-Rao lower bounds for estimating the infected degree distribution in the case of Erdos-Rényi and also power law (scale free) networks such as Twitter. In comparison, [78] provides a stochastic approximation algorithm and analysis on a Hilbert space for tracking the degree distribution of evolving random networks with a duplication-deletion model.…”

Section: Related Literaturementioning

confidence: 99%

Dynamics of Information Diffusion and Social Sensing

Krishnamurthy

Hoiles²

2018

Cooperative and Graph Signal Processing

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Statistical inference using social sensors is an area that has witnessed remarkable progress in the last decade. It is relevant in a variety of applications including localizing events for targeted advertising, marketing, localization of natural disasters and predicting sentiment of investors in financial markets. This chapter presents a tutorial description of four important aspects of sensing-based information diffusion in social networks from a communications/signal processing perspective. First, diffusion models for information exchange in large scale social networks together with social sensing via social media networks such as Twitter is considered. Second, Bayesian social learning models and risk averse social learning is considered with applications in finance and online reputation systems. Third, the principle of revealed preferences arising in micro-economics theory is used to parse datasets to determine if social sensors are utility maximizers and then determine their utility functions. Finally, the interaction of social sensors with YouTube channel owners is studied using time series analysis methods. All four topics are explained in the context of actual experimental datasets from health networks, social media and psychological experiments. Also, algorithms are given that exploit the above models to infer underlying events based on social sensing. The overview, insights, models and algorithms presented in this chapter stem from recent developments in network science, economics and signal processing. At a deeper level, this chapter considers mean field dynamics of networks, risk averse Bayesian social learning filtering and quickest change detection, data incest in decision making over a directed acyclic graph of social sensors, inverse optimization problems for utility function estimation (revealed preferences) and statistical modeling of interacting social sensors in YouTube social networks.

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“…However, as real world networks are time evolving, we extend the analysis of diffusion thresholds to time evolving networks using generative models for the underlying network evolution. [25] provides a stochastic approximation algorithm and analysis on a Hilbert space for tracking the degree distribution of evolving random networks with a duplication-deletion model. There are various generative models for large real world networks in the literature, see [26], [27], [25], and the references therein.…”

Section: Literaturementioning

confidence: 99%

“…[25] provides a stochastic approximation algorithm and analysis on a Hilbert space for tracking the degree distribution of evolving random networks with a duplication-deletion model. There are various generative models for large real world networks in the literature, see [26], [27], [25], and the references therein. In this paper, we consider one such model, namely, the preferential attachment model [26], and analyze the connection between the diffusion threshold and the parameters that dictate evolution.…”

Section: Literaturementioning

confidence: 99%