Learning Linear Influence Models in Social Networks from Transient Opinion Dynamics

Abstract

Social networks, forums, and social media have emerged as global platforms for forming and shaping opinions on a broad spectrum of topics like politics, sports, and entertainment. Users (also called actors ) often update their evolving opinions, influenced through discussions with other users. Theoretical models and their analysis on understanding opinion dynamics in social networks abound in the literature. However, these models are often based on concepts from statistical physics. Their goal is to establish specific phenomena like steady state consensus or bifurcation. Analysis of transient effects is largely avoided. Moreover, many of these studies assume that actors’ opinions are observed globally and synchronously, which is rarely realistic. In this article, we initiate an investigation into a family of novel data-driven influence models that accurately learn and fit realistic observations. We estimate and do not presume edge strengths from observed opinions at nodes. Our influence models are linear but not necessarily positive or row stochastic in nature. As a consequence, unlike the previous studies, they do not depend on system stability or convergence during the observation period. Furthermore, our models take into account a wide variety of data collection scenarios. In particular, they are robust to missing observations for several timesteps after an actor has changed its opinion. In addition, we consider scenarios where opinion observations may be available only for aggregated clusters of nodes—a practical restriction often imposed to ensure privacy. Finally, to provide a conceptually interpretable design of edge influence, we offer a relatively frugal variant of our influence model, where the strength of influence between two connecting nodes depends on the node attributes (demography, personality, expertise, etc.). Such an approach reduces the number of model parameters, reduces overfitting, and offers a tractable and explicable sketch of edge influences in the context of opinion dynamics. With six real-life datasets crawled from Twitter and Reddit, as well as three more datasets collected from in-house experiments (with 102 volunteers), our proposed system gives a significant accuracy boost over four state-of-the-art baselines.