One-shot Distributed Ridge Regression in High Dimensions
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:8763-8772, 2020.
To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental problem in this area: How to do ridge regression in a distributed computing environment? We study one-shot methods constructing weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high dimensional model where each predictor has a small effect, we discover several new phenomena including that the efficiency depends strongly on the signal strength, but does not degrade with many workers, the risk decouples over machines, and the unexpected consequence that the optimal weights do not sum to unity. We also propose a new optimally weighted one-shot ridge regression algorithm. Our results are supported by simulations and real data analysis.