Centroid Approximation for Bootstrap

Mao Ye, qiang liu

Keywords: bootstrap, centroid approximation, uncertainty

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.

One-sentence Summary: We propose a centroid approximation for bootstrap that improves the quality of bootstrap when the number of bootstrap particles is small.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2110.08720/code)