# A Survey on Uncertainty Quantification Methods for Deep Learning

arXiv: https://arxiv.org/abs/2302.13425 · HTML: https://mlsanity.com/paper/2302.13425/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- Builds on 86 of its 241 references that are in the map.
- First posted on arXiv 26 Feb 2023.

## Builds on (most cited first, 30 of 86)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [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)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)

## Built on by (most cited first, 30 of 81)

- [Towards Trustworthy Retrieval Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2502.06872/) (2025)
- [From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered](https://mlsanity.com/paper/2506.07461/) (2025)
- [Calibration in Machine Learning Uncertainty Quantification: beyond consistency to target adaptivity](https://mlsanity.com/paper/2309.06240/) (2023)
- [Graph-based Confidence Calibration for Large Language Models](https://mlsanity.com/paper/2411.02454/) (2024)
- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)
- [Position: Epistemic uncertainty estimation methods are fundamentally incomplete](https://mlsanity.com/paper/2505.23506/) (2025)
- [Hallucination in Multimodal Foundation Models: A Survey on Causes, Corrections, and Evaluations](https://mlsanity.com/paper/2410.15359/) (2024)
- [Scale-Dropout: Estimating Uncertainty in Deep Neural Networks Using Stochastic Scale](https://mlsanity.com/paper/2311.15816/) (2023)
- [Rethinking the Uncertainty: A Critical Review and Analysis in the Era of Large Language Models](https://mlsanity.com/paper/2410.20199/) (2024)
- [ProcCtrlBench: Evaluating Process-Level Defects and Control Preservation in LLM Coding Agents](https://mlsanity.com/paper/2605.20251/) (2026)
- [Validation of uncertainty quantification metrics: a primer based on the consistency and adaptivity concepts](https://mlsanity.com/paper/2303.07170/) (2023)
- [Evidential Uncertainty Estimation for Multi-Modal Trajectory Prediction](https://mlsanity.com/paper/2503.05274/) (2025)
- [Uncertainty Unveiled: Can Exposure to More In-context Examples Mitigate Uncertainty for Large Language Models?](https://mlsanity.com/paper/2505.21003/) (2025)
- [Comparing Uncertainty Measurement and Mitigation Methods for Large Language Models: A Systematic Review](https://mlsanity.com/paper/2504.18346/) (2025)
- [A Narrative Review on Large AI Models in Lung Cancer Screening, Diagnosis, and Treatment Planning](https://mlsanity.com/paper/2506.07236/) (2025)
- [Uncovering the Fragility of Trustworthy LLMs through Chinese Textual Ambiguity](https://mlsanity.com/paper/2507.23121/) (2025)
- [Building Real-time Awareness of Out-of-distribution in Trajectory Prediction for Autonomous Vehicles](https://mlsanity.com/paper/2409.17277/) (2024)
- [Uncertainty in a Single Pass: A Closed-Form Identity for One-Step Flow Matching](https://mlsanity.com/paper/2605.00941/) (2026)
- [Old Rules in a New Game: Mapping Uncertainty Quantification to Quantum Machine Learning](https://mlsanity.com/paper/2507.14919/) (2025)
- [PyHealth 2.0: A Comprehensive Open-Source Toolkit for Accessible and Reproducible Clinical Deep Learning](https://mlsanity.com/paper/2601.16414/) (2026)
- [Deep Learning for Spatiotemporal Big Data: A Vision on Opportunities and Challenges](https://mlsanity.com/paper/2310.19957/) (2023)
- [Spatial Knowledge-Infused Hierarchical Learning: An Application in Flood Mapping on Earth Imagery](https://mlsanity.com/paper/2312.07767/) (2023)
- [Uncertainty Quantification for Deep Learning](https://mlsanity.com/paper/2405.20550/) (2024)
- [Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions](https://mlsanity.com/paper/2503.12354/) (2025)
- [Polymer Data Challenges in the AI Era: Bridging Gaps for Next-Generation Energy Materials](https://mlsanity.com/paper/2505.13494/) (2025)
- [Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators](https://mlsanity.com/paper/2507.14652/) (2025)
- [Probabilistic Consistency in Machine Learning and Its Connection to Uncertainty Quantification](https://mlsanity.com/paper/2507.21670/) (2025)
- [Deep Learning-Based Analysis of Power Consumption in Gasoline, Electric, and Hybrid Vehicles](https://mlsanity.com/paper/2508.08034/) (2025)
- [Evaluating the Quality of the Quantified Uncertainty for (Re)Calibration of Data-Driven Regression Models](https://mlsanity.com/paper/2508.17761/) (2025)
- [Analyzing Uncertainty Quantification in Statistical and Deep Learning Models for Probabilistic Electricity Price Forecasting](https://mlsanity.com/paper/2509.19417/) (2025)

## Abstract (arXiv)

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to serious consequences in high-stakes applications such as autonomous driving, medical diagnosis, and disaster response. Uncertainty quantification (UQ) estimates the confidence of DNN predictions in addition to their accuracy. In recent years, many UQ methods have been developed for DNNs. It is valuable to systematically categorize these methods and compare their strengths and limitations. Existing surveys mostly categorize UQ methodologies by neural network architecture or Bayesian formulation, while overlooking the uncertainty sources each method addresses, making it difficult to select an appropriate approach in practice. To fill this gap, this paper presents a taxonomy of UQ methods for DNNs based on uncertainty sources (e.g., data versus model uncertainty). We summarize the advantages and disadvantages of each category, and illustrate how UQ can be applied to machine learning problems (e.g., active learning, out-of-distribution robustness, and deep reinforcement learning). We also identify future research directions, including UQ for large language models (LLMs), AI-driven scientific simulations, and deep neural networks with structured outputs.