  We investigate and compare the fundamental performance of several distributed
learning methods that have been proposed recently. We do this in the context of
a distributed version of the classical signal-in-Gaussian-white-noise model,
which serves as a benchmark model for studying performance in this setting. The
results show how the design and tuning of a distributed method can have great
impact on convergence rates and validity of uncertainty quantification.
Moreover, we highlight the difficulty of designing nonparametric distributed
procedures that automatically adapt to smoothness.
