Centroid Approximation for Bootstrap: Improving Particle Quality at Inference
This addresses the bottleneck of computational intensity for uncertainty quantification in deep learning, offering a more efficient solution.
The paper tackles the computational inefficiency of standard bootstrap methods in large-scale machine learning by proposing an optimization-based approach using centroid points to approximate the ideal bootstrap distribution, achieving more accurate uncertainty estimation with fewer samples.
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.