[Paper Review] A Stochastic Differential Equation Framework for Guiding Information Diffusion

Yichen Wang, Evangelos A. Theodorou+2 more|arXiv (Cornell University)|Mar 30, 2016

Opinion Dynamics and Social Influence3 citations

TL;DR

This paper proposes a unified stochastic differential equation (SDE) framework to model and control information diffusion in networks, accommodating noisy data, time-varying edges, and node births. It enables faster convergence, lower variance, and reduced control cost compared to alternatives, effectively steering both stable and unstable diffusion processes to desired states.

ABSTRACT

The information content of a node in information networks is influenced by its neighbors in the networks. Recently there has been much work on modeling information diffusion, but few has integrated these models for online decision making. A framework for guiding information diffusion is critically important for understanding the vulnerabilities of these networks and designing good policies to suppress rumors and misinformation. Here, we propose an unified stochastic differential equation framework for modeling information diffusion over networks and designing the control policy to guide such diffusion. Our framework can handle noisy data, networks with time-varying edges and node birth processes. Using both synthetic and real world networks, we showed that our framework is robust, able to steer both stable and unstable information diffusion systems to desired states with faster convergence, less variance and lower control cost than alternatives.

Motivation & Objective

• To develop a unified framework that models information diffusion in complex networks with dynamic and uncertain structures.
• To integrate modeling and control for online decision-making in information diffusion processes.
• To address vulnerabilities in networks by enabling effective suppression of rumors and misinformation.
• To design a control policy that ensures fast convergence and low variance in both stable and unstable diffusion systems.
• To minimize control cost while maintaining robustness under noisy and time-varying network conditions.

Proposed method

• Formulates a stochastic differential equation (SDE) framework to model the evolution of information content across network nodes.
• Incorporates node-level information dynamics influenced by neighboring nodes through a mean-field approximation.
• Integrates control inputs into the SDE to steer the system toward desired diffusion states.
• Handles time-varying network topologies by modeling edge changes as stochastic processes within the SDE framework.
• Accounts for noisy observations and node birth processes by embedding measurement and birth processes into the SDE dynamics.
• Employs numerical solvers and optimization techniques to compute control policies that minimize cost while achieving target states.

Experimental results

Research questions

• RQ1 How can a unified framework model information diffusion in networks with time-varying edges and noisy data?
• RQ2 Can the proposed SDE framework effectively control both stable and unstable information diffusion processes?
• RQ3 What is the performance of the control policy in terms of convergence speed, variance, and control cost compared to existing methods?
• RQ4 How does the framework handle node birth processes and dynamic network structures in real-world settings?
• RQ5 To what extent does the framework improve robustness and efficiency in suppressing misinformation?

Key findings

• The proposed SDE framework successfully models information diffusion in networks with time-varying edges and noisy data.
• The framework enables faster convergence to desired diffusion states compared to alternative methods.
• It achieves lower variance in the diffusion process, indicating more stable control performance.
• The control policy results in significantly reduced control cost across both synthetic and real-world networks.
• The framework maintains robust performance under dynamic network conditions, including node births and edge changes.
• Empirical evaluation on real and synthetic networks confirms superior performance in steering unstable systems to target states.