2019/03/21 by Edgar Dobriban, Sheng Yue, Dobriban, Edgar +2
Computer Science · Engineering · Mathematics · #Computation (stat.CO) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and Algorithms #Machine Learning and ELM #Parallel #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1903.09321
openalex publication_date 2019/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In many areas, practitioners need to analyze large datasets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental and highly important problem in this area: How to do ridge regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high dimensional random-effects model where each predictor has a small effect, we discover several new phenomena. 1. Infinite-worker limit: The distributed estimator works well for very large numbers of machines, a phenomenon we call "infinite-worker limit". 2. Optimal weights: The optimal weights for combining local estimators sum to more than unity, due to the downward bias of ridge. Thus, all averaging methods are suboptimal. We also propose a new Weighted ONe-shot DistributEd Ridge regression (WONDER) algorithm. We test WONDER in simulation studies and using the Million Song Dataset as an example. There it can save at least 100x in computation time, while nearly preserving test accuracy.