  The problem of communicating sensor measurements over shared networks is
prevalent in many modern large-scale distributed systems such as cyber-physical
systems, wireless sensor networks, and the internet of things. Due to bandwidth
constraints, the system designer must jointly design decentralized medium
access transmission and estimation policies that accommodate a very large
number of devices in extremely contested environments such that the collection
of all observations is reproduced at the destination with the best possible
fidelity. We formulate a remote estimation problem in the mean-field regime
where a very large number of sensors communicate their observations to an
access point, or base station, under a strict constraint on the maximum
fraction of transmitting devices. We show that in the mean-field regime, this
problem exhibits a structure that enables tractable optimization algorithms.
More importantly, we obtain a data-driven learning scheme that admits a finite
sample-complexity guarantee on the performance of the resulting estimation
system under minimal assumptions on the data's probability density function.
