Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics. However, due to its nature of multiple training and resampling, bootstrapping deep neural networks is computationally burdensome; hence it has difficulties in practical application to the uncertainty estimation and related tasks. To overcome this computational bottleneck, we propose a novel approach called Neural Bootstrapper (NeuBoots), which learns to generate bootstrapped neural networks through single model training. NeuBoots injects the bootstrap weights into the high-level feature layers of the backbone network and outputs the bootstrapped predictions of the target, without additional parameters and the repetitive computations from scratch. We apply NeuBoots to various machine learning tasks related to uncertainty quantification, including prediction calibrations in image classification and semantic segmentation, active learning, and detection of out-of-distribution samples. Our empirical results show that NeuBoots outperforms other bagging based methods under a much lower computational cost without losing the validity of bootstrapping.

Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics.

We remark that the Dirichlet distribution with a uniform parameter of one can be easily approximated by independent exponential distribution. We use this block bootstrap as a default of the NeuBoots in sequel. We shall rigorously investigate asymptotic equivalence between the blocked bootstrap and the non-blocked bootstrap. To ease the explanation for theory, we introduce some notation here. Recall that the notation is introduced in Section 2 .[

Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics.

Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics. However, due to its nature of multiple training and resampling, bootstrapping deep neural networks is computationally burdensome; hence it has difficulties in practical application to the uncertainty estimation and related tasks. To overcome this computational bottleneck, we propose a novel approach called Neural Bootstrapper (NeuBoots), which learns to generate bootstrapped neural networks through single model training. NeuBoots injects the bootstrap weights into the high-level feature layers of the backbone network and outputs the bootstrapped predictions of the target, without additional parameters and the repetitive computations from scratch. We apply NeuBoots to various machine learning tasks related to uncertainty quantification, including prediction calibrations in image classification and semantic segmentation, active learning, and detection of out-of-distribution samples. Our empirical results show that NeuBoots outperforms other bagging based methods under a much lower computational cost without losing the validity of bootstrapping.

Bootstrapping has been a primary tool for uncertainty quantification, and their theoretical and computational properties have been investigated in the field of statistics and machine learning. However, due to its nature of repetitive computations, the computational burden required to implement bootstrap procedures for the neural network is painfully heavy, and this fact seriously hurdles the practical use of these procedures on the uncertainty estimation of modern deep learning. To overcome the inconvenience, we propose a procedure called Neural Bootstrapper (NeuBoots). We reveal that the NeuBoots stably generate valid bootstrap samples that coincide with the desired target samples with minimal extra computational cost compared to traditional bootstrapping. Consequently, NeuBoots makes it feasible to construct bootstrap confidence intervals of outputs of neural networks and quantify their predictive uncertainty. We also suggest NeuBoots for deep convolutional neural networks to consider its utility in image classification tasks, including calibration, detection of out-of-distribution samples, and active learning. Empirical results demonstrate that NeuBoots is significantly beneficial for the above purposes. Since the introduction of the nonparametric bootstrap (Efron, 1979), bootstrap (or bagging) procedures have been commonly used as a primary tool in quantifying uncertainty lying on statistical inference, e.g.