Appears in collection : 2016 - T1 - WS3 - Central workshop

We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. For the case of Gaussian distributions, we provide tight tradeoffs (up to logarithmic factors) between the estimation error and the communication required, for both sparse and dense mean estimation. The main tool is strong data processing inequalities, which are well studied in the information theory literature. We generalize these to distributed data processing inequalities.