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