# Comparing the quality of neural network uncertainty estimates for classification problems

arXiv: https://arxiv.org/abs/2308.05903 · HTML: https://mlsanity.com/paper/2308.05903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 9 of 9)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Uncertainty Baselines: Benchmarks for Uncertainty & Robustness in Deep Learning](https://mlsanity.com/paper/2106.04015/) (2021)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Empirical Frequentist Coverage of Deep Learning Uncertainty Quantification Procedures](https://mlsanity.com/paper/2010.03039/) (2020)

## Abstract (arXiv)

Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature due to their usefulness in decision making, particularly for high-consequence decisions. However, there has been little research done on how to evaluate the quality of such methods. We use statistical methods of frequentist interval coverage and interval width to evaluate the quality of credible intervals, and expected calibration error to evaluate classification predicted confidence. These metrics are evaluated on Bayesian neural networks (BNN) fit using Markov Chain Monte Carlo (MCMC) and variational inference (VI), bootstrapped neural networks (NN), Deep Ensembles (DE), and Monte Carlo (MC) dropout. We apply these different UQ for DL methods to a hyperspectral image target detection problem and show the inconsistency of the different methods' results and the necessity of a UQ quality metric. To reconcile these differences and choose a UQ method that appropriately quantifies the uncertainty, we create a simulated data set with fully parameterized probability distribution for a two-class classification problem. The gold standard MCMC performs the best overall, and the bootstrapped NN is a close second, requiring the same computational expense as DE. Through this comparison, we demonstrate that, for a given data set, different models can produce uncertainty estimates of markedly different quality. This in turn points to a great need for principled assessment methods of UQ quality in DL applications.