Probabilistic models for network growth, change point detection and emergence of self-organization through reinforcement
Abstract
The last few years have witnessed an explosion in the amount of empirical data on real networks motivating an array of mathematical models for the evolution of such networks. The sub-discipline of Dynamic networks has started to play an increasingly important role yet poses significant mathematical challenges. Motivations include (a) distributed schemes to solve large scale numerical optimization problems over enormous data; (b) statistical estimation and change point detection of dynamic network models; (c) simple probabilistic rules such as social opinion dynamics that in simulations lead to the emergence of fascinating macroscopic order of consensus and polarization; (d) systems of interacting agents with limited computational capacities such as simple sensors; (e) mathematical models in biological systems such as networks of interacting neurons. This proposal has three main research aims: (a) Probabilistic and statistical theory for generative network models: Evolving network models have become one of the standard workhorses in the empirical networks community. There is a dearth of rigorous methodology to inform practitioners regarding estimation of the driving parameters of the models in the evolution of the network. We propose to develop theoretical techniques using continuous time branching processes. These techniques also extend to understanding the effect of abrupt changes in the driving parameters of the model. (b) Self organization in Dynamic network models: development of theory related to the emergence of macroscopic order via simple reinforcement rules; this includes fixation of leaders, individuals with maximal social influence as well as Bose-Einstein condensation in networks. (c) Distributed and decentralized optimization: Theory for stochastic gradient algorithms in distributed settings, motivated by the exponential growth of data will be developed. Connections to fundamental probabilistic systems such as reinforced random walks will be explored. Theory will be developed for adaptive networks where nodes observe streaming data and are entrusted with statistical learning of driving parameteres. Continuum scaling limits of such models in social network models and networks of interacting spiking neurons will be studied. Pedagogy development and cross-domain collaborations: (a) A major component of the proposal is undergraduate education in particular the development of a first year undergraduate research seminar course. (b) Projects developed in the course will lead to summer research projects with high school students at the NC School of Science and Math. (c) Graduate students supported by the grant will be used to mentor both undergraduates and high school students. (d) A number of questions in the grant arose through collaborations with domain experts including political scientists here at UNC and data from the UNC Department of Genetics. Theory developed in the grant will inform practice.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1710010
Entities
People
- Shankar Bhamidi
Organizations
- Army Contracting Command
- United States Army
- University of North Carolina at Chapel Hill