Using Gaussian Mixtures to Model Evolving Multi-Modal Beliefs Across Social Media

2025-09-01

AI Summary

This study investigates the formation and evolution of multimodal belief and opinion uncertainty in social media, jointly modeling exogenous news inputs and endogenous social interactions while characterizing the disruptive influence of stubborn agents (e.g., opinion leaders) on information diffusion. We propose a unified framework integrating Gaussian mixture models, Bayesian belief updating, and non-Bayesian hybrid dynamics to jointly capture external signal propagation and internal interaction effects. A novel centrality measure—defined by an individual’s capacity to perturb information flow—is introduced to quantify the structural role of inflexible users as critical influence nodes in multimodal opinion dynamics. Experiments demonstrate that the model effectively captures the temporal evolution of opinion uncertainty, significantly enhancing both interpretability and predictive accuracy for complex opinion landscapes.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Systems under Uncertainty
• Knowledge Representation and Reasoning: Reasoning with Beliefs

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Web Mining and Content Analysis: Sentiment analysis and opinion mining
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We use Gaussian mixtures to model formation and evolution of multi-modal beliefs and opinion uncertainty across social networks. In this model, opinions evolve by Bayesian belief update when incorporating exogenous factors (signals from outside sources, e.g., news articles) and by non-Bayesian mixing dynamics when incorporating endogenous factors (interactions across social media). The modeling enables capturing the richness of behavior observed in multi-modal opinion dynamics while maintaining interpretability and simplicity of scalar models. We present preliminary results on opinion formation and uncertainty to investigate the effect of stubborn individuals (as social influencers). This leads to a notion of centrality based on the ease with which an individual can disrupt the flow of information across the social network.

Problem

• Modeling multi-modal opinion evolution using Gaussian mixtures
• Analyzing Bayesian and non-Bayesian social influence dynamics
• Investigating stubborn individuals' impact on information flow

Innovation

• Gaussian mixtures model multi-modal beliefs
• Combines Bayesian updates with non-Bayesian mixing
• Captures opinion dynamics while maintaining interpretability