This article addresses novel real-valued consensus problems in the presence of malicious adversaries that can move within the network and induce faulty behaviors in the attacked agents. By adopting several mobile adversary models from the computer science literature, we develop protocols which can mitigate the influence of such malicious agents. The algorithms follow the class of mean subsequence reduced (MSR) algorithms, under which agents ignore the suspicious values received from neighbors during their state updates. Different from the static adversary models, even after the adversaries move away, the infected agents may remain faulty in their values, whose effects must be taken into account. We develop conditions on the network structures for both the complete and non-complete directed graph cases, under which the proposed algorithms are guaranteed to attain resilient consensus. The tolerance bound for network conditions becomes more strict as the adversaries are allowed to have more power. Extensive simulations are carried out over random graphs to verify the effectiveness of our approach when the information of the adversarial agents in terms of their models and numbers is unknown to the agents.

Collaborative computing is efficient to conduct large-scale computation tasks, especially with the surge in data volume. However, when the data contains sensitive information, privacy has to be attached significant attention during the execution of computation tasks. In this paper, based on a two-step average computation framework, we first propose three different privacy-aware schemes, where noises are carefully designed to be injected into the distributed computing process. The challenging issue is to guarantee the privacy loss in each iteration to be controllable and quantifiable, which we call the dynamic privacy-preserving collaborative computing problem. By employing Kullback-Leibler differential privacy, we obtain the privacy preserving levels in different iterations regarding the three schemes, followed by the analysis of their convergence performances. Further, we devise an approach to balance the privacy loss and the computation accuracy, whose challenge lies in how to motivate data contributors (DCs) to report more accurate data without providing them with monetized payments. This is done by allowing DCs to report data multiple times, and we obtain the optimal reporting times for each DC. Finally, extensive numerical experiments are performed to validate the obtained theoretical results.

In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or past observations. Additionally, we discover that in order to achieve the prediction error bounds asymptotically, the necessary and sufficient condition is that the “innovation” is asymptotically white Gaussian. When restricted to Gaussian processes and 1-step prediction, our bounds are shown to reduce to the Kolmogorov-Szegö formula and Wiener-Masani formula known from linear prediction theory.