  This paper proposes a distributed Gaussian process regression (GPR) with
over-the-air computation, termed AirComp GPR, for communication- and
computation-efficient data analysis over wireless networks. GPR is a
non-parametric regression method that can model the target flexibly. However,
its computational complexity and communication efficiency tend to be
significant as the number of data increases. AirComp GPR focuses on that
product-of-experts-based GPR approximates the exact GPR by a sum of values
reported from distributed nodes. We introduce AirComp for the training and
prediction steps to allow the nodes to transmit their local computation results
simultaneously; the communication strategies are presented, including
distributed training based on perfect and statistical channel state information
cases. Applying to a radio map construction task, we demonstrate that AirComp
GPR speeds up the computation time while maintaining the communication cost in
training constant regardless of the numbers of data and nodes.
