Many social networks are characterized by actors (nodes) holding quantitative opinions about movies, songs, sports, people, colleges, politicians, and so on. These opinions are influenced by network neighbors. Many models have been proposed for such opinion dynamics, but they have some limitations. Most consider the strength of edge influence as fixed. Some model a discrete decision or action on part of each actor, and an edge as causing an ``infection'' (that is often permanent or self-resolving). Others model edge influence as a stochastic matrix to reuse the mathematics of eigensystems. Actors' opinions are usually observed globally and synchronously. Analysis usually skirts transient effects and focuses on steady-state behavior. There is very little direct experimental validation of estimated influence models. Here we initiate an investigation into new models that seek to remove these limitations. Our main goal is to estimate, not assume, edge influence strengths from an observed series of opinion values at nodes. We adopt a linear (but not stochastic) influence model. We make no assumptions about system stability or convergence. Further, actors' opinions may be observed in an asynchronous and incomplete fashion, after missing several time steps when an actor changed its opinion based on neighbors' influence. We present novel algorithms to estimate edge influence strengths while tackling these aggressively realistic assumptions. Experiments with Reddit, Twitter, and three social games we conducted on volunteers establish the promise of our algorithms. Our opinion estimation errors are dramatically smaller than strong baselines like the DeGroot, flocking, voter, and biased voter models. Our experiments also lend qualitative insights into asynchronous opinion updates and aggregation.
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