Distributed estimation through parallel approximants

TL;DR

This paper introduces a scalable framework for distributed estimation using parallel approximants, enabling efficient analysis of large data sets without requiring all data to be in memory.

Contribution

It formalizes a class of statistics suitable for distributed computation and demonstrates how to approximate functional operators, expanding scalable estimation methods.

Findings

Provides a formal framework for distributed estimators.

Shows how to approximate functional operators in distributed settings.

Includes implementations for quantile calculation and local polynomial regression.

Abstract

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 $L^2$ 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.