# Dense Uncertainty Estimation

arXiv: https://arxiv.org/abs/2110.06427 · HTML: https://mlsanity.com/paper/2110.06427/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 125 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 30 of 73)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [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)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Unsupervised Monocular Depth Estimation with Left-Right Consistency](https://mlsanity.com/paper/1609.03677/) (2016)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [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)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [Rethinking ImageNet Pre-training](https://mlsanity.com/paper/1811.08883/) (2018)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Anabranch Network for Camouflaged Object Segmentation](https://mlsanity.com/paper/2105.09451/) (2021)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)

## Built on by (most cited first, 9 of 9)

- [Behavioral Intention Prediction in Driving Scenes: A Survey](https://mlsanity.com/paper/2211.00385/) (2022)
- [The Treasure Beneath Multiple Annotations: An Uncertainty-aware Edge Detector](https://mlsanity.com/paper/2303.11828/) (2023)
- [Are we certain it's anomalous?](https://mlsanity.com/paper/2211.09224/) (2022)
- [Disentangling Uncertainty in Machine Translation Evaluation](https://mlsanity.com/paper/2204.06546/) (2022)
- [On the Overconfidence Problem in Semantic 3D Mapping](https://mlsanity.com/paper/2311.10018/) (2023)
- [Segmentation-based Assessment of Tumor-Vessel Involvement for Surgical Resectability Prediction of Pancreatic Ductal Adenocarcinoma](https://mlsanity.com/paper/2310.00639/) (2023)
- [A General Divergence Modeling Strategy for Salient Object Detection](https://mlsanity.com/paper/2111.11827/) (2021)
- [R^2-HGP: A Double-Regularized Gaussian Process for Heterogeneous Transfer Learning](https://mlsanity.com/paper/2512.10258/) (2025)
- [Uncertainty-Driven Replay Memory for Reinforcement Learning](https://mlsanity.com/paper/2608.29860/) (2026)

## Abstract (arXiv)

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the weights, which leads to deterministic predictions during testing. In this way, a specific weights set is estimated while ignoring any uncertainty that may occur in the proper weight space. The latter introduces randomness into the framework, either by assuming a prior distribution over model parameters (i.e. Bayesian Neural Networks) or including latent variables (i.e. generative models) to explore the contribution of latent variables for model predictions, leading to stochastic predictions during testing. Different from the former that achieves point estimation, the latter aims to estimate the prediction distribution, making it possible to estimate uncertainty, representing model ignorance about its predictions. We claim that conventional deterministic neural network based dense prediction tasks are prone to overfitting, leading to over-confident predictions, which is undesirable for decision making. In this paper, we investigate stochastic neural networks and uncertainty estimation techniques to achieve both accurate deterministic prediction and reliable uncertainty estimation. Specifically, we work on two types of uncertainty estimations solutions, namely ensemble based methods and generative model based methods, and explain their pros and cons while using them in fully/semi/weakly-supervised framework. Due to the close connection between uncertainty estimation and model calibration, we also introduce how uncertainty estimation can be used for deep model calibration to achieve well-calibrated models, namely dense model calibration. Code and data are available at https://github.com/JingZhang617/UncertaintyEstimation.