# Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression

arXiv: https://arxiv.org/abs/2308.09065 · HTML: https://mlsanity.com/paper/2308.09065/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 82 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 30 of 51)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [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)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [AdaBins: Depth Estimation using Adaptive Bins](https://mlsanity.com/paper/2011.14141/) (2020)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimation](https://mlsanity.com/paper/1907.10326/) (2019)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Benchmarking Robustness in Object Detection: Autonomous Driving when Winter is Coming](https://mlsanity.com/paper/1907.07484/) (2019)
- [Sparsity Invariant CNNs](https://mlsanity.com/paper/1708.06500/) (2017)
- [Addressing Failure Prediction by Learning Model Confidence](https://mlsanity.com/paper/1910.04851/) (2019)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [Augmented Reality Meets Computer Vision : Efficient Data Generation for Urban Driving Scenes](https://mlsanity.com/paper/1708.01566/) (2017)
- [Benchmarking the Robustness of Semantic Segmentation Models](https://mlsanity.com/paper/1908.05005/) (2019)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)

## Built on by (most cited first, 7 of 7)

- [On the Calibration of Human Pose Estimation](https://mlsanity.com/paper/2311.17105/) (2023)
- [SurvUnc: A Meta-Model Based Uncertainty Quantification Framework for Survival Analysis](https://mlsanity.com/paper/2505.14803/) (2025)
- [Towards Trustworthy Vital Sign Forecasting: Leveraging Uncertainty for Prediction Intervals](https://mlsanity.com/paper/2509.01319/) (2025)
- [Collision Risk Estimation via Loss Prediction in End-to-End Autonomous Driving](https://mlsanity.com/paper/2503.07425/) (2025)
- [Robust Uncertainty Estimation under Distribution Shift via Difference Reconstruction](https://mlsanity.com/paper/2601.19341/) (2026)
- [From Calibration to Refinement: Seeking Certainty via Probabilistic Evidence Propagation for Noisy-Label Person Re-Identification](https://mlsanity.com/paper/2602.23133/) (2026)
- [CUPID: A Plug-in Framework for Joint Aleatoric and Epistemic Uncertainty Estimation with a Single Model](https://mlsanity.com/paper/2603.10745/) (2026)

## Abstract (arXiv)

Uncertainty quantification is critical for deploying deep neural networks (DNNs) in real-world applications. An Auxiliary Uncertainty Estimator (AuxUE) is one of the most effective means to estimate the uncertainty of the main task prediction without modifying the main task model. To be considered robust, an AuxUE must be capable of maintaining its performance and triggering higher uncertainties while encountering Out-of-Distribution (OOD) inputs, i.e., to provide robust aleatoric and epistemic uncertainty. However, for vision regression tasks, current AuxUE designs are mainly adopted for aleatoric uncertainty estimates, and AuxUE robustness has not been explored. In this work, we propose a generalized AuxUE scheme for more robust uncertainty quantification on regression tasks. Concretely, to achieve a more robust aleatoric uncertainty estimation, different distribution assumptions are considered for heteroscedastic noise, and Laplace distribution is finally chosen to approximate the prediction error. For epistemic uncertainty, we propose a novel solution named Discretization-Induced Dirichlet pOsterior (DIDO), which models the Dirichlet posterior on the discretized prediction error. Extensive experiments on age estimation, monocular depth estimation, and super-resolution tasks show that our proposed method can provide robust uncertainty estimates in the face of noisy inputs and that it can be scalable to both image-level and pixel-wise tasks. Code is available at https://github.com/ENSTA-U2IS/DIDO .