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Bootstrap is a principled and powerful frequentist statistical tool foruncertainty quantification. Unfortunately, standard bootstrap methods arecomputationally intensive due to the need of drawing a large i.i.d. bootstrapsample to approximate the ideal bootstrap distribution; this largely hinderstheir application in large-scale machine learning, especially deep learningproblems. In this work, we propose an efficient method to explicitly\emph{optimize} a small set of high quality ``centroid'' points to betterapproximate the ideal bootstrap distribution. We achieve this by minimizing asimple objective function that is asymptotically equivalent to the Wassersteindistance to the ideal bootstrap distribution. This allows us to provide anaccurate estimation of uncertainty with a small number of bootstrap centroids,outperforming the naive i.i.d. sampling approach. Empirically, we show that ourmethod can boost the performance of bootstrap in a variety of applications.

Centroid Approximation for Bootstrap: Improving Particle Quality at Inference