Optimality guarantees for distributed statistical estimation
This work addresses the challenge of efficient distributed computation for large datasets, providing theoretical guarantees that are incremental but precise for statistical estimation tasks.
The paper tackles the problem of distributed statistical estimation with limited communication between machines, establishing lower bounds on the communication required to match centralized minimax risk for various problems like location estimation and regression models.
Large data sets often require performing distributed statistical estimation, with a full data set split across multiple machines and limited communication between machines. To study such scenarios, we define and study some refinements of the classical minimax risk that apply to distributed settings, comparing to the performance of estimators with access to the entire data. Lower bounds on these quantities provide a precise characterization of the minimum amount of communication required to achieve the centralized minimax risk. We study two classes of distributed protocols: one in which machines send messages independently over channels without feedback, and a second allowing for interactive communication, in which a central server broadcasts the messages from a given machine to all other machines. We establish lower bounds for a variety of problems, including location estimation in several families and parameter estimation in different types of regression models. Our results include a novel class of quantitative data-processing inequalities used to characterize the effects of limited communication.