  We consider the problem of privately estimating the mean of vectors
distributed across different nodes of an unreliable wireless network, where
communications between nodes can fail intermittently. We adopt a
semi-decentralized setup, wherein to mitigate the impact of intermittently
connected links, nodes can collaborate with their neighbors to compute a local
consensus, which they relay to a central server. In such a setting, the
communications between any pair of nodes must ensure that the privacy of the
nodes is rigorously maintained to prevent unauthorized information leakage. We
study the tradeoff between collaborative relaying and privacy leakage due to
the data sharing among nodes and, subsequently, propose PriCER: Private
Collaborative Estimation via Relaying -- a differentially private collaborative
algorithm for mean estimation to optimize this tradeoff. The privacy guarantees
of PriCER arise (i) implicitly, by exploiting the inherent stochasticity of the
flaky network connections, and (ii) explicitly, by adding Gaussian
perturbations to the estimates exchanged by the nodes. Local and central
privacy guarantees are provided against eavesdroppers who can observe different
signals, such as the communications amongst nodes during local consensus and
(possibly multiple) transmissions from the relays to the central server. We
substantiate our theoretical findings with numerical simulations. Our
implementation is available at
https://github.com/rajarshisaha95/private-collaborative-relaying.
