2021/12/31 by Aritra Chakravorty, Chakravorty, Aritra, William S. Cleveland +3
Computer Science · Engineering · Physics and Astronomy · #62B10 #62G05 (Primary) 62G05 #65Y05 #68W10 #68W15 (Secondary) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Model Reduction and Neural Networks #Parallel #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2112.15572
openalex publication_date 2021/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the entirety of very large, distributed data sets. We first formalize the class of statistics which admit straightforward calculation in distributed environments through independent parallelization. We then show how to use such statistics to approximate arbitrary functional operators in appropriate spaces, yielding a general estimation framework that does not require data to reside entirely in memory. We characterize the L2 approximation properties of our approach and provide fully implemented examples of sample quantile calculation and local polynomial regression in a distributed computing environment. A variety of avenues and extensions remain open for future work.