From mobile phones, through autonomous vehicles, to geographically spread-out data centers – modern distributed networks generate an abundance of data each day. Communication constraints and privacy concerns may prohibit sending the data to a central server to be jointly analyzed. This brings forth a novel challenge: how to jointly learn from data distributed across servers while keeping the communication costs low. In this talk, I’ll describe a distributed parametric estimation problem in which this goal is achievable. I’ll present a simple algorithm where each server sends only a short message to the center. While each server fails the estimation task with high probability, a central server can still learn from these messages and correctly estimate the parameter. Moreover, the total communication cost is not only lower than sending the entire distributed dataset, but even lower than just sending the data located on a single server.