Information Value on Private State Inference in Network Systems

Abstract In network systems, neighboring nodes usually need to exchange and update their state information iteratively to achieve a global computation and control goal. Considering the nodes’ states may include some sensitive/private information, e.g., location and income, different random mechanizes have been proposed to preserve the privacy of the states. However, no matter what type of random mechanisms is used, the eavesdropping attacker can infer/estimate a node’s state based on the information it holds, and the estimation depends on the available information. The relationship between the estimation and the information is a critical and open issue. Therefore, in this paper, we investigate how to obtain the optimal estimation of a node’s state with available information and how to quantify the value of the information in the state inference. First, we exploit a utility function to quantify the utility of the estimation accuracy, and then the optimal estimation and information value are defined to depict the estimation and quantify the information, respectively. Next, the optimal estimation under different settings of the noise and utility function is provided. Lastly, we obtain some essential properties of information value and analyze the value of state outputs in distributed algorithms.