# Nonparametric Uncertainty Quantification for Single Deterministic Neural Network

arXiv: https://arxiv.org/abs/2202.03101 · HTML: https://mlsanity.com/paper/2202.03101/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 84 references that are in the map.
- First posted on arXiv 7 Feb 2022.

## Builds on (most cited first, 29 of 29)

- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [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)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [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)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [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)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [An Evaluation Dataset for Intent Classification and Out-of-Scope Prediction](https://mlsanity.com/paper/1909.02027/) (2019)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [Ensemble Distribution Distillation](https://mlsanity.com/paper/1905.00076/) (2019)
- [Can Autonomous Vehicles Identify, Recover From, and Adapt to Distribution Shifts?](https://mlsanity.com/paper/2006.14911/) (2020)
- [Greedy Policy Search: A Simple Baseline for Learnable Test-Time Augmentation](https://mlsanity.com/paper/2002.09103/) (2020)
- [Likelihood Ratios and Generative Classifiers for Unsupervised Out-of-Domain Detection In Task Oriented Dialog](https://mlsanity.com/paper/1912.12800/) (2019)
- [Uncertainty Modelling in Deep Networks: Forecasting Short and Noisy Series](https://mlsanity.com/paper/1807.09011/) (2018)

## Built on by (most cited first, 30 of 36)

- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agents](https://mlsanity.com/paper/2505.22655/) (2025)
- [Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistency](https://mlsanity.com/paper/2502.04964/) (2025)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Uncertainty Quantification in LLM Agents: Foundations, Emerging Challenges, and Opportunities](https://mlsanity.com/paper/2602.05073/) (2026)
- [Token-Level Density-Based Uncertainty Quantification Methods for Eliciting Truthfulness of Large Language Models](https://mlsanity.com/paper/2502.14427/) (2025)
- [On Information-Theoretic Measures of Predictive Uncertainty](https://mlsanity.com/paper/2410.10786/) (2024)
- [A Data-Driven Measure of Relative Uncertainty for Misclassification Detection](https://mlsanity.com/paper/2306.01710/) (2023)
- [Density-Softmax: Efficient Test-time Model for Uncertainty Estimation and Robustness under Distribution Shifts](https://mlsanity.com/paper/2302.06495/) (2023)
- [Uncertainty Quantification with the Empirical Neural Tangent Kernel](https://mlsanity.com/paper/2502.02870/) (2025)
- [Uncertainty Estimation by Flexible Evidential Deep Learning](https://mlsanity.com/paper/2510.18322/) (2025)
- [Density-Regression: Efficient and Distance-Aware Deep Regressor for Uncertainty Estimation under Distribution Shifts](https://mlsanity.com/paper/2403.05600/) (2024)
- [Tilt your Head: Activating the Hidden Spatial-Invariance of Classifiers](https://mlsanity.com/paper/2405.03730/) (2024)
- [Uncertainty-aware abstention in medical diagnosis based on medical texts](https://mlsanity.com/paper/2502.18050/) (2025)
- [Uncertainty Quantification for Regression using Proper Scoring Rules](https://mlsanity.com/paper/2509.26610/) (2025)
- [Unsupervised Variational Translator for Bridging Image Restoration and High-Level Vision Tasks](https://mlsanity.com/paper/2408.08149/) (2024)
- [Holistic Uncertainty Estimation For Open-Set Recognition](https://mlsanity.com/paper/2408.14229/) (2024)
- [Beyond the Norms: Detecting Prediction Errors in Regression Models](https://mlsanity.com/paper/2406.06968/) (2024)
- [Uncertainty Quantification for Regression: A Unified Framework based on kernel scores](https://mlsanity.com/paper/2510.25599/) (2025)
- [Learning Invariant Representations with a Nonparametric Nadaraya-Watson Head](https://mlsanity.com/paper/2309.13377/) (2023)
- [Combining Statistical Depth and Fermat Distance for Uncertainty Quantification](https://mlsanity.com/paper/2404.08476/) (2024)
- [Efficient Nearest Neighbor based Uncertainty Estimation for Natural Language Processing Tasks](https://mlsanity.com/paper/2407.02138/) (2024)
- [Integrating uncertainty quantification into randomized smoothing based robustness guarantees](https://mlsanity.com/paper/2410.20432/) (2024)
- [Probabilistic Modeling of Disparity Uncertainty for Robust and Efficient Stereo Matching](https://mlsanity.com/paper/2412.18703/) (2024)
- [Who to Trust? Aggregating Client Predictions in Federated Distillation](https://mlsanity.com/paper/2509.15147/) (2025)

## Abstract (arXiv)

This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions. First, we show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's nonparametric estimate of the conditional label distribution. Importantly, the proposed approach allows to disentangle explicitly aleatoric and epistemic uncertainties. The resulting method works directly in the feature space. However, one can apply it to any neural network by considering an embedding of the data induced by the network. We demonstrate the strong performance of the method in uncertainty estimation tasks on text classification problems and a variety of real-world image datasets, such as MNIST, SVHN, CIFAR-100 and several versions of ImageNet.