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Social networks often exert social pressure, causing individuals to adapttheir expressed opinions to conform to their peers. An agent in such systemscan be modeled as having a (true and unchanging) inherent belief whilebroadcasting a declared opinion at each time step based on her inherent beliefand the past declared opinions of her neighbors. An important question in thissetting is parameter estimation: how to disentangle the effects of socialpressure to estimate inherent beliefs from declared opinions. This is usefulfor forecasting when agents' declared opinions are influenced by socialpressure while real-world behavior only depends on their inherent beliefs. Toaddress this, Jadbabaie et al. formulated the Interacting P\'olya Urn model ofopinion dynamics under social pressure and studied it on complete-graph socialnetworks using an aggregate estimator, and found that their estimator convergesto the inherent beliefs unless majority pressure pushes the network toconsensus.  In this work, we studythis model on arbitrary networks, providing anestimator which converges to the inherent beliefs even in consensus situations.Finally, we bound the convergence rate of our estimator in both consensus andnon-consensus scenarios; to get the bound for consensus scenarios (whichconverge slower than non-consensus) we additionally found how quickly thesystem converges to consensus.

Estimating True Beliefs in Opinion Dynamics with Social Pressure