Centroid Approximation for Bootstrap: Improving Particle Quality at Inference

TL;DR

This paper introduces a novel centroid-based bootstrap approximation method that reduces computational costs and improves uncertainty estimation accuracy in large-scale machine learning and deep learning applications.

Contribution

The authors propose an optimization-based approach to select high-quality bootstrap centroids, enhancing the efficiency and accuracy of bootstrap uncertainty quantification.

Findings

Outperforms naive i.i.d. bootstrap sampling in accuracy

Reduces computational costs for bootstrap in large-scale settings

Improves uncertainty estimation in various applications

Abstract

Bootstrap is a principled and powerful frequentist statistical tool for uncertainty quantification. Unfortunately, standard bootstrap methods are computationally intensive due to the need of drawing a large i.i.d. bootstrap sample to approximate the ideal bootstrap distribution; this largely hinders their application in large-scale machine learning, especially deep learning problems. In this work, we propose an efficient method to explicitly \emph{optimize} a small set of high quality ``centroid'' points to better approximate the ideal bootstrap distribution. We achieve this by minimizing a simple objective function that is asymptotically equivalent to the Wasserstein distance to the ideal bootstrap distribution. This allows us to provide an accurate estimation of uncertainty with a small number of bootstrap centroids, outperforming the naive i.i.d. sampling approach. Empirically, we show that our method can boost the performance of bootstrap in a variety of applications.