  This paper studies social system inference from a single trajectory of public
evolving opinions, wherein observation noise leads to the statistical
dependence of samples on time and coordinates. We first propose a cyber-social
system that comprises individuals in a social network and a set of information
sources in a cyber layer, whose opinion dynamics explicitly takes confirmation
bias, novelty bias and process noise into account. Based on the proposed social
model, we then study the sample complexity of least-square auto-regressive
model estimation, which governs the number of observations that are sufficient
for the identified model to achieve the prescribed levels of accuracy and
confidence. Building on the identified social model, we then investigate social
inference, with particular focus on the weighted network topology, the
subconscious bias and the model parameters of confirmation bias and novelty
bias. Finally, the theoretical results and the effectiveness of the proposed
social model and inference algorithm are validated by the US Senate Member
Ideology data.
