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View Submission - SDS2022
Title: Distributed estimation through parallel approximants Authors:  Patrick Wolfe - Purdue University (United States) [presenting]
Aritra Chakravorty - Purdue University (United States)
William S Cleveland - Purdue University (United States)
Abstract: Designing estimation algorithms that use the entirety of very large data sets is a core challenge in modern statistics. We provide a framework to address this challenge based on parallel approximants, which in turn yields scalable algorithms with accompanying consistency guarantees. Rather than employ approaches based on sampling, we instead 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 generic approximate inference procedures that do not require data to reside entirely in memory. We characterize the $L^2$ approximation properties of our approach, and discuss some canonical examples. A variety of avenues and extensions remain open for future work.