A Stochastic Differential Equation Framework for Guiding Online User Activities in Closed Loop

Our opinion is influenced by those of others we connect to in social networks. How to model opinion dynamics across social networks and can we steer the public opinion to a desired state? Answers to these questions are critically important for understanding the vulnerabilities of online social networks and increasing their resilience to rumor and false information. Recently there has been much work on modeling the dynamics in information diffusion, but few work has integrated these models into a systematic control framework. In this paper, we propose a unified multivariate jump diffusion process framework for modeling opinion dynamics over networks and determining the control over such networks. Our method can handle noisy and partially observed data, and over networks with time-varying and node birth processes. Using synthetic and real world networks, we showed that our framework is robust, able to control both stable and unstable dynamics systems with fast convergence speed, less variance and low control cost.