# A Comparison of the Delta Method and the Bootstrap in Deep Learning Classification

arXiv: https://arxiv.org/abs/2107.01606 · HTML: https://mlsanity.com/paper/2107.01606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 14 references that are in the map.
- First posted on arXiv 4 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Deterministic Implementations for Reproducibility in Deep Reinforcement Learning](https://mlsanity.com/paper/1809.05676/) (2018)

## Abstract (arXiv)

We validate the recently introduced deep learning classification adapted Delta method by a comparison with the classical Bootstrap. We show that there is a strong linear relationship between the quantified predictive epistemic uncertainty levels obtained from the two methods when applied on two LeNet-based neural network classifiers using the MNIST and CIFAR-10 datasets. Furthermore, we demonstrate that the Delta method offers a five times computation time reduction compared to the Bootstrap.