Interactive Inference under Information Constraints

TL;DR

This paper investigates how interactivity influences distributed statistical inference under constraints like privacy and communication, providing new bounds and demonstrating scenarios where interactivity offers advantages.

Contribution

It introduces a unified approach to derive lower bounds for interactive protocols in distribution testing and estimation under information constraints.

Findings

Established optimal bounds for estimation and testing under privacy and communication constraints.

Identified cases where interactivity improves inference performance.

Provided a new method to handle correlations in interactive protocols.

Abstract

We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. We focus on the tasks of goodness-of-fit testing and estimation of discrete distributions. From prior work, these tasks are well understood under noninteractive protocols. Extending these approaches directly for interactive protocols is difficult due to correlations that can build due to interactivity; in fact, gaps can be found in prior claims of tight bounds of distribution estimation using interactive protocols. We propose a new approach to handle this correlation and establish a unified method to establish lower bounds for both tasks. As an application, we obtain optimal bounds for both estimation and testing under local differential privacy and communication constraints. We also provide an example of a natural testing problem where interactivity helps.