  We develop a privacy-preserving distributed projection least mean squares
(LMS) strategy over linear multitask networks, where agents' local parameters
of interest or tasks are linearly related. Each agent is interested in not only
improving its local inference performance via in-network cooperation with
neighboring agents, but also protecting its own individual task against privacy
leakage. In our proposed strategy, at each time instant, each agent sends a
noisy estimate, which is its local intermediate estimate corrupted by a
zero-mean additive noise, to its neighboring agents. We derive a sufficient
condition to determine the amount of noise to add to each agent's intermediate
estimate to achieve an optimal trade-off between the network
mean-square-deviation and an inference privacy constraint. We propose a
distributed and adaptive strategy to compute the additive noise powers, and
study the mean and mean-square behaviors and privacy-preserving performance of
the proposed strategy. Simulation results demonstrate that our strategy is able
to balance the trade-off between estimation accuracy and privacy preservation.
