In recent years, the amount of available information has become so vast in certain fields of applications that it is infeasible or undesirable to carry out all the computations on a single server. This has motivated the design and study of distributed statistical or learning approaches. In distributed methods, the data is split amongst different administrative units and computations are carried out locally in parallel to each other. The outcome of the local computations are then aggregated into a final result on a central machine.
In this talk we will consider the limitations and guarantees of distributed methods under communication constraints (i.e. only limited amount of bits are allowed to be transmitted between the machines) in context of the random design regression model. We derive minimax lower bounds, matching upper bounds and provide adaptive estimators reaching these limits.
This is a joint work with Harry van Zanten.