  Batch training of machine learning models based on neural networks is now
well established, whereas to date streaming methods are largely based on linear
models. To go beyond linear in the online setting, nonparametric methods are of
interest due to their universality and ability to stably incorporate new
information via convexity or Bayes' Rule. Unfortunately, when used online,
nonparametric methods suffer a "curse of dimensionality" which precludes their
use: their complexity scales at least with the time index. We survey online
compression tools which bring their memory under control and attain approximate
convergence. The asymptotic bias depends on a compression parameter that trades
off memory and accuracy. Further, the applications to robotics, communications,
economics, and power are discussed, as well as extensions to multi-agent
systems.
