Adaptive distributed methods under communication constraints

In this paper we take up the study of the fundamental possibilities and limitations of distributed methods for high-dimensional, or nonparametric problems. The design and study of such methods has attracted substantial attention recently. This is for a large part motivated by the ever increasing size of datasets, leading to the necessity to analyze data while distributed over multiple machines and/or cores. Other reasons to consider distributed methods include privacy considerations or the simple fact that in some situations data are physically collected at multiple locations. By now a variety of methods are available for estimating nonparametric or highdimensional models to data in a distributed manner.