# Uncertainty Quantification for Deep Learning

arXiv: https://arxiv.org/abs/2405.20550 · HTML: https://mlsanity.com/paper/2405.20550/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 11 of 11)

- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [MetNet: A Neural Weather Model for Precipitation Forecasting](https://mlsanity.com/paper/2003.12140/) (2020)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Notes on the Behavior of MC Dropout](https://mlsanity.com/paper/2008.02627/) (2020)
- [Learnable Histogram: Statistical Context Features for Deep Neural Networks](https://mlsanity.com/paper/1804.09398/) (2018)

## Built on by (most cited first, 1 of 1)

- [The Ensemble Kalman Inversion Race](https://mlsanity.com/paper/2511.15853/) (2025)

## Abstract (arXiv)

We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework for uncertainty quantification in deep learning that accounts for all major sources of uncertainty: input data, training and testing data, neural network weights, and machine-learning model imperfections, targeting regression problems. We systematically quantify each source by applying Bayes' theorem and conditional probability densities and introduce a fast, practical implementation method. We demonstrate its effectiveness on a simple regression problem and a real-world application: predicting cloud autoconversion rates using a neural network trained on aircraft measurements from the Azores and guided by a two-moment bin model of the stochastic collection equation. In this application, uncertainty from the training and testing data dominates, followed by input data, neural network model, and weight variability. Finally, we highlight the practical advantages of this methodology, showing that explicitly modeling training data uncertainty improves robustness to new inputs that fall outside the training data, and enhances model reliability in real-world scenarios.