## Centroid Approximation for Bootstrap: Improving Particle Quality at Inference

### Mao Ye · Qiang Liu

##### Hall E #713

Keywords: [ MISC: Scalable Algorithms ]

[ Abstract ]
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Wed 20 Jul 3:30 p.m. PDT — 5:30 p.m. PDT

Spotlight presentation: PM: Variational Inference/Bayesian Models and Methods
Wed 20 Jul 7:30 a.m. PDT — 9 a.m. PDT

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.

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