Optimally Compressed Nonparametric Online Learning

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 classic "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 while attaining approximate convergence. The asymptotic bias depends on a compression parameter which trades off memory and accuracy, echoing Shannon-Nyquist sampling for nonparametric statistics. Applications to autonomous robotics, communications, economics, and power are scoped, as well as extensions to multi-agent systems.