SIAM News Blog

Modeling Opinion Dynamics in Social Networks

By Lina Sorg

In today’s technologically-advanced society, social networking dominates how people exchange information and interact with each other. Active individuals on sites like Facebook and Twitter share breaking or controversial news almost immediately, initiating near-instantaneous discussion and debate among users. As a result, many users’ personal ideas are influenced by those of their vocal peers, so much so that political campaigns often monitor trending opinions on social networking sites. 

In a talk entitled “Learning Opinion Dynamics in Social Networks,” part of a minisymposium at the SIAM Annual Meeting, Manuel Gomez Rodriguez (Max Planck Institute for Software Systems) presented a probabilistic framework, called SLANT, to model opinion dynamics. “When you have an opinion expressed, you can usually say whether it’s positive or negative,” Rodriguez said. However, though researchers can immediately discern a noisy estimate of a user’s current opinion on a certain topic, the influence of that user’s opinion—and the influence of other users’ opinions of that user—is generally hidden. “We’re interested in trying to predict how your opinion may be changing,” he said, “as well as distinguishing between informational and temporal influences.”

The goal in developing SLANT was to design a realistic model that fits real fine-grained opinion traces, predicts opinions overtime, and reveals how opinions influence one another. “There are a lot of theoretical models of opinion dynamics, but not many that distinguish between latent and expressed opinions,” Rodriguez said. “And opinions are not updated sequentially in discrete time.” As a consequence, existing models do not learn from fine-grained data and thus often yield inaccurate predictions. Rodriguez’s framework models each user’s messages as a marked point process to keep track of opinions. In this way, the model follows stubborn users, compromised users, and conforming users, enabling a theoretical analysis of both the transient and steady state. 

Rodriguez's model scales to networks with millions of nodes and events.
Rodriguez identifies a set of conditions that steadily unites users’ opinions, calculates a linear relation between the steady-state and initial opinions, and adapts an efficient sampling algorithm for multivariate Hawkes processes that was introduced in 2015. His resulting equation—in which the instantaneous message intensity (i.e. the number of tweets or “likes” per hour) is the rate—includes both message history and increases in the number of messages/tweets/likes used to share information. A user’s message intensity comprises messages by his/her own initiative, temporal influences from user to user, and previous message history. 

Rodriguez then created a method of estimation based on historical diffusion of data that scales to networks with millions of nodes and events. He evaluated SLANT with network data from real-world events, such as the upcoming United States presidential elections, and tested his model on sites like Twitter, Amazon, and Reddit. For each dataset, Rodriguez built a collection of events to fit and evaluate the model. Although forecasted opinions become less accurate as the time increases, results indicated that SLANT fits online communication data accurately and may provide more precise predictions than prior methods. Rodriguez hopes to explore questions of nonlinear dependence and the development of opinion control methods as he continues work on his model. 

   Lina Sorg is the associate editor of SIAM News
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