Biblio

We study a model where a data collector obtains data from users through a payment mechanism to learn the underlying state from the elicited data. The private signal of each user represents her individual knowledge about the state. Through social interactions, each user can also learn noisy versions of her friends' signals, which is called group signals. Based on both her private signal and group signals, each user makes strategic decisions to report a privacy-preserved version of her data to the data collector. We develop a Bayesian game theoretic framework to study the impact of social learning on users' data reporting strategies and devise the payment mechanism for the data collector accordingly. Our findings reveal that, the Bayesian-Nash equilibrium can be in the form of either a symmetric randomized response (SR) strategy or an informative non-disclosive (ND) strategy. A generalized majority voting rule is applied by each user to her noisy group signals to determine which strategy to follow. When a user plays the ND strategy, she reports privacy-preserving data completely based on her group signals, independent of her private signal, which indicates that her privacy cost is zero. Both the data collector and the users can benefit from social learning which drives down the privacy costs and helps to improve the state estimation at a given payment budget. We derive bounds on the minimum total payment required to achieve a given level of state estimation accuracy.

The large amounts of synchrophasor data obtained by Phasor Measurement Units (PMUs) provide dynamic visibility into power systems. Extracting reliable information from the data can enhance power system situational awareness. The data quality often suffers from data losses, bad data, and cyber data attacks. Data privacy is also an increasing concern. In this paper, we discuss our recently proposed framework of data recovery, error correction, data privacy enhancement, and event identification methods by exploiting the intrinsic low-dimensional structures in the high-dimensional spatial-temporal blocks of PMU data. Our data-driven approaches are computationally efficient with provable analytical guarantees. The data recovery method can recover the ground-truth data even if simultaneous and consecutive data losses and errors happen across all PMU channels for some time. We can identify PMU channels that are under false data injection attacks by locating abnormal dynamics in the data. The data recovery method for the operator can extract the information accurately by collectively processing the privacy-preserving data from many PMUs. A cyber intruder with access to partial measurements cannot recover the data correctly even using the same approach. A real-time event identification method is also proposed, based on the new idea of characterizing an event by the low-dimensional subspace spanned by the dominant singular vectors of the data matrix.