An asymptotic analysis of distributed nonparametric methods

Both in statistics and machine learning there has been substantial interest in the design and study of distributed statistical or learning methods in recent years. One driving reason is the fact that in certain applications datasets have become so large that it is often unfeasible, or computationally undesirable, to carry out the analysis on a single machine. In a distributed method the data are divided over a cluster consisting of several machines and/or cores. The machines in the cluster then process their data locally, after which the local results are somehow aggregated on a central machine to finally produce the overall outcome of the statistical analysis. Distributed methods are not only used for computational reasons, but are for instance also of interest in situations where privacy is important and it is undesirable that all data are handled at a single location. Moreover, there are applications in which data are by construction gathered at multiple locations and first processed locally, before being combined at a central location. Over the last years a variety of distributed methods have been proposed. Recent examples include Consensus Monte Carlo (Scott et al. (2016)), WASP The research leading to these results has received funding from the Netherlands Science foundation NWO and from the European Research Council under ERC Grant Agreement 320637.