# A Survey on Uncertainty Reasoning and Quantification for Decision Making: Belief Theory Meets Deep Learning

arXiv: https://arxiv.org/abs/2206.05675 · HTML: https://mlsanity.com/paper/2206.05675/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 137 references that are in the map.
- First posted on arXiv 12 Jun 2022.

## Builds on (most cited first, 20 of 20)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Uncertainty-Aware Deep Classifiers using Generative Models](https://mlsanity.com/paper/2006.04183/) (2020)
- [Multivariate Uncertainty in Deep Learning](https://mlsanity.com/paper/1910.14215/) (2019)
- [An evidential classifier based on Dempster-Shafer theory and deep learning](https://mlsanity.com/paper/2103.13549/) (2021)
- [Multidimensional Uncertainty-Aware Evidential Neural Networks](https://mlsanity.com/paper/2012.13676/) (2020)
- [Quantifying Classification Uncertainty using Regularized Evidential Neural Networks](https://mlsanity.com/paper/1910.06864/) (2019)
- [Deep Learning for Predicting Dynamic Uncertain Opinions in Network Data](https://mlsanity.com/paper/1910.05640/) (2019)
- [Justification-Based Reliability in Machine Learning](https://mlsanity.com/paper/1911.07391/) (2019)
- [Boosting Cross-Lingual Transfer via Self-Learning with Uncertainty Estimation](https://mlsanity.com/paper/2109.00194/) (2021)
- [SEED: Sound Event Early Detection via Evidential Uncertainty](https://mlsanity.com/paper/2202.02441/) (2022)
- [Variational Encoder-based Reliable Classification](https://mlsanity.com/paper/2002.08289/) (2020)

## Built on by (most cited first, 6 of 6)

- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [Rethinking the Uncertainty: A Critical Review and Analysis in the Era of Large Language Models](https://mlsanity.com/paper/2410.20199/) (2024)
- [Knowledge-enhanced Neural Machine Reasoning: A Review](https://mlsanity.com/paper/2302.02093/) (2023)
- [Evidential Federated Learning for Skin Lesion Image Classification](https://mlsanity.com/paper/2411.10071/) (2024)

## Abstract (arXiv)

An in-depth understanding of uncertainty is the first step to making effective decisions under uncertainty. Deep/machine learning (ML/DL) has been hugely leveraged to solve complex problems involved with processing high-dimensional data. However, reasoning and quantifying different types of uncertainties to achieve effective decision-making have been much less explored in ML/DL than in other Artificial Intelligence (AI) domains. In particular, belief/evidence theories have been studied in KRR since the 1960s to reason and measure uncertainties to enhance decision-making effectiveness. We found that only a few studies have leveraged the mature uncertainty research in belief/evidence theories in ML/DL to tackle complex problems under different types of uncertainty. In this survey paper, we discuss several popular belief theories and their core ideas dealing with uncertainty causes and types and quantifying them, along with the discussions of their applicability in ML/DL. In addition, we discuss three main approaches that leverage belief theories in Deep Neural Networks (DNNs), including Evidential DNNs, Fuzzy DNNs, and Rough DNNs, in terms of their uncertainty causes, types, and quantification methods along with their applicability in diverse problem domains. Based on our in-depth survey, we discuss insights, lessons learned, limitations of the current state-of-the-art bridging belief theories and ML/DL, and finally, future research directions.