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Wyner-Ziv Estimators: Efficient Distributed Mean Estimation with Side Information
Communication efficient distributed mean estimation is an important primitive
that arises in many distributed learning and optimization scenarios such as
federated learning. Without any probabilistic assumptions on the underlying
data, we study the problem of distributed mean estimation where the server has
access to side information. We propose \emph{Wyner-Ziv estimators}, which are
communication and computationally efficient and near-optimal when an upper
bound for the distance between the side information and the data is known. As a
corollary, we also show that our algorithms provide efficient schemes for the
classic Wyner-Ziv problem in information theory. In a different direction, when
there is no knowledge assumed about the distance between side information and
the data, we present an alternative Wyner-Ziv estimator that uses correlated
sampling. This latter setting offers {\em universal recovery guarantees}, and
perhaps will be of interest in practice when the number of users is large and
keeping track of the distances between the data and the side information may
not be possible