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.