Inference under Information Constraints II: Communication Constraints and Shared Randomness

Understand

A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center.

• We study problems of distribution learning and identity testing in this distributed inference setting and examine the role of shared randomness as a resource.
• We propose a general-purpose simulate-and-infer strategy that uses only private-coin communication protocols and is sample-optimal for distribution learning.
• This general strategy turns out to be sample-optimal even for distribution testing among private-coin protocols.