Collaboratively Learning Linear Models with Structured Missing Data

We study the problem of collaboratively learning least squares estimates for m agents. Each agent observes a different subset of the features---e.g., containing data collected from sensors of varying resolution. Our goal is to determine how to coordinate the agents in order to produce the best estimator for each agent. We propose a distributed, semi-supervised algorithm Collab, consisting of three steps: local training, aggregation, and distribution. Our procedure does not require communicating the labeled data, making it communication efficient and useful in settings where the labeled data is inaccessible.