Title: Preserving Data-Privacy with Added Noises: Optimal Estimation and Privacy Analysis,
Abstract: Networked system often relies on distributed algorithms to achieve a global
computation goal with iterative local information exchanges between neighbor
nodes. To preserve data privacy, a node may add a random noise to its original
data for information exchange at each iteration. Nevertheless, a neighbor node
can estimate other's original data based on the information it received. The
estimation accuracy and data privacy can be measured in terms of $(\epsilon,
\delta)$-data-privacy, defined as the probability of $\epsilon$-accurate
estimation (the difference of an estimation and the original data is within
$\epsilon$) is no larger than $\delta$ (the disclosure probability). How to
optimize the estimation and analyze data privacy is a critical and open issue.
In this paper, a theoretical framework is developed to investigate how to
optimize the estimation of neighbor's original data using the local information
received, named optimal distributed estimation. Then, we study the disclosure
probability under the optimal estimation for data privacy analysis. We further
apply the developed framework to analyze the data privacy of the
privacy-preserving average consensus algorithm and identify the optimal noises
for the algorithm.