Collaboratively Learning Linear Models with Structured Missing Data

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Collaborative Learning, Missing Data, Sensors, Linear Regression
Abstract: 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. Despite this handicap, our procedure is nearly asymptotically, local-minimax optimal---even among estimators allowed to communicate the labeled data such as imputation methods. We test our method on US Census data. We also discuss generalizations of our method to non-Gaussian feature settings, non-linear settings, and Federated Learning.
Supplementary Material: pdf
Submission Number: 9257