On Communication Cost of Distributed Statistical Estimation and Dimensionality

Understand

We explore the connection between dimensionality and communication cost in distributed learning problems.

• Specifically we study the problem of estimating the mean $\vec{\theta}$ of an unknown $d$ dimensional gaussian distribution in the distributed setting.
• In this problem, the samples from the unknown distribution are distributed among $m$ different machines.
• The goal is to estimate the mean $\vec{\theta}$ at the optimal minimax rate while communicating as few bits as possible.