Nonparametric Bayesian Aggregation for Massive Data

Abstract

We develop a set of scalable Bayesian inference procedures for a general class of nonparametric regression models. Specifically, nonparametric Bayesian inferences are separately performed on each subset randomly split from a massive dataset, and then the obtained local results are aggregated into global counterparts. This aggregation step is explicit without involving any additional computation cost. By a careful partition, we show that our aggregated inference results obtain an oracle rule in the sense that they are equivalent to those obtained directly from the entire data (which are computationally prohibitive). For example, an aggregated credible ball achieves desirable credibility level and also frequentist coverage while possessing the same radius as the oracle ball.

A Divide-and-Conquer Bayesian Approach to Large-Scale Kriging

“…We show that when k is controlled to increase in some proper order of n as n tends to infinity, the Bayes L 2 -risk of the DISK posterior achieves near minimax optimal convergence rates under different types of covariance functions. There are some theoretical results in this direction (Shang and Cheng, 2015, Cheng and Shang, 2017, Szabo and van Zanten, 2017, but DISK is the first general Bayesian framework addressing these theoretical problems with a focus on computationally efficient posterior computations in massive data applications with complex nonparametric models, while avoiding restrictive assumptions that limit wide applicability.…”