Centroid Approximation for Bootstrap: Improving Particle Quality at Inference

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 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.

Authors

• Mao Ye 0006
• Qiang Liu 0001

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