# Sampling-free Epistemic Uncertainty Estimation Using Approximated Variance Propagation

arXiv: https://arxiv.org/abs/1908.00598 · HTML: https://mlsanity.com/paper/1908.00598/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2019.

## Built on by (most cited first, 30 of 74)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [SHIFT: A Synthetic Driving Dataset for Continuous Multi-Task Domain Adaptation](https://mlsanity.com/paper/2206.08367/) (2022)
- [On the Practicality of Deterministic Epistemic Uncertainty](https://mlsanity.com/paper/2107.00649/) (2021)
- [Triggering Failures: Out-Of-Distribution detection by learning from local adversarial attacks in Semantic Segmentation](https://mlsanity.com/paper/2108.01634/) (2021)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safety](https://mlsanity.com/paper/2104.14235/) (2021)
- [ValUES: A Framework for Systematic Validation of Uncertainty Estimation in Semantic Segmentation](https://mlsanity.com/paper/2401.08501/) (2024)
- [Robust Semantic Segmentation with Superpixel-Mix](https://mlsanity.com/paper/2108.00968/) (2021)
- [CertainNet: Sampling-free Uncertainty Estimation for Object Detection](https://mlsanity.com/paper/2110.01604/) (2021)
- [ZigZag: Universal Sampling-free Uncertainty Estimation Through Two-Step Inference](https://mlsanity.com/paper/2211.11435/) (2022)
- [Detection of out-of-distribution samples using binary neuron activation patterns](https://mlsanity.com/paper/2212.14268/) (2022)
- [Blurs Behave Like Ensembles: Spatial Smoothings to Improve Accuracy, Uncertainty, and Robustness](https://mlsanity.com/paper/2105.12639/) (2021)
- [DEBOSH: Deep Bayesian Shape Optimization](https://mlsanity.com/paper/2109.13337/) (2021)
- [Deep Probability Estimation](https://mlsanity.com/paper/2111.10734/) (2021)
- [Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributions](https://mlsanity.com/paper/2105.04471/) (2021)
- [STUN: Self-Teaching Uncertainty Estimation for Place Recognition](https://mlsanity.com/paper/2203.01851/) (2022)
- [Trust Your Robots! Predictive Uncertainty Estimation of Neural Networks with Sparse Gaussian Processes](https://mlsanity.com/paper/2109.09690/) (2021)
- [STUaNet: Understanding uncertainty in spatiotemporal collective human mobility](https://mlsanity.com/paper/2102.06027/) (2021)
- [Uncertainty Estimation for Molecules: Desiderata and Methods](https://mlsanity.com/paper/2306.14916/) (2023)
- [Enabling Uncertainty Estimation in Iterative Neural Networks](https://mlsanity.com/paper/2403.16732/) (2024)
- [UncTrack: Reliable Visual Object Tracking with Uncertainty-Aware Prototype Memory Network](https://mlsanity.com/paper/2503.12888/) (2025)
- [Uncertainty-Aware Credit Card Fraud Detection Using Deep Learning](https://mlsanity.com/paper/2107.13508/) (2021)
- [Unsupervised confidence for LiDAR depth maps and applications](https://mlsanity.com/paper/2210.03118/) (2022)
- [Uncertainty Quantification via Stable Distribution Propagation](https://mlsanity.com/paper/2402.08324/) (2024)
- [Learned Hallucination Detection in Black-Box LLMs using Token-level Entropy Production Rate](https://mlsanity.com/paper/2509.04492/) (2025)
- [Dense Uncertainty Estimation](https://mlsanity.com/paper/2110.06427/) (2021)
- [Segmenting Known Objects and Unseen Unknowns without Prior Knowledge](https://mlsanity.com/paper/2209.05407/) (2022)
- [Multi-view 3D Object Reconstruction and Uncertainty Modelling with Neural Shape Prior](https://mlsanity.com/paper/2306.11739/) (2023)
- [Learning Uncertainty For Safety-Oriented Semantic Segmentation In Autonomous Driving](https://mlsanity.com/paper/2105.13688/) (2021)
- [Concurrent Misclassification and Out-of-Distribution Detection for Semantic Segmentation via Energy-Based Normalizing Flow](https://mlsanity.com/paper/2305.09610/) (2023)

## Abstract (arXiv)

We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents how much one can trust predictions on new data. Recently promising works were proposed using noise injection combined with Monte-Carlo sampling at inference time to estimate this quantity (e.g. Monte-Carlo dropout). Our main contribution is an approximation of the epistemic uncertainty estimated by these methods that does not require sampling, thus notably reducing the computational overhead. We apply our approach to large-scale visual tasks (i.e., semantic segmentation and depth regression) to demonstrate the advantages of our method compared to sampling-based approaches in terms of quality of the uncertainty estimates as well as of computational overhead.