Social System Inference from Noisy Observations

This article studies social system inference from a single noisy 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 the asymmetric cognitive bias including confirmation bias and negativity bias and the process noise into account. Based on the proposed cyber-social model, we then study the sample complexity of least-square auto-regressive model estimation, which governs the length of a single observed trajectory that is sufficient for the identified model to achieve the prescribed levels of accuracy and confidence (PAC). Building on the identified social model, we then investigate social inference, with a particular focus on the weighted network topology and the model parameters of asymmetric cognitive bias. Finally, the theoretical results and the effectiveness of the proposed inference framework are validated by the U.S. Senate Member Ideology data.