# Density estimation in representation space to predict model uncertainty

arXiv: https://arxiv.org/abs/1908.07235 · HTML: https://mlsanity.com/paper/1908.07235/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2019.

## Built on by (most cited first, 27 of 27)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Learning to Intervene on Concept Bottlenecks](https://mlsanity.com/paper/2308.13453/) (2023)
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- [Gradient-Based Quantification of Epistemic Uncertainty for Deep Object Detectors](https://mlsanity.com/paper/2107.04517/) (2021)
- [Better with Less: A Data-Active Perspective on Pre-Training Graph Neural Networks](https://mlsanity.com/paper/2311.01038/) (2023)
- [Evidential Uncertainty Quantification: A Variance-Based Perspective](https://mlsanity.com/paper/2311.11367/) (2023)
- [A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learning](https://mlsanity.com/paper/2406.00332/) (2024)
- [Concurrent Misclassification and Out-of-Distribution Detection for Semantic Segmentation via Energy-Based Normalizing Flow](https://mlsanity.com/paper/2305.09610/) (2023)
- [Probabilistic Machine Learning for Noisy Labels in Earth Observation](https://mlsanity.com/paper/2504.03478/) (2025)
- [What is Flagged in Uncertainty Quantification? Latent Density Models for Uncertainty Categorization](https://mlsanity.com/paper/2207.05161/) (2022)
- [Uncertainty-Aware Deep Learning for Wildfire Danger Forecasting](https://mlsanity.com/paper/2509.25017/) (2025)
- [TEDL: A Two-stage Evidential Deep Learning Method for Classification Uncertainty Quantification](https://mlsanity.com/paper/2209.05522/) (2022)
- [An Exploratory Study of AI System Risk Assessment from the Lens of Data Distribution and Uncertainty](https://mlsanity.com/paper/2212.06828/) (2022)
- [Accuracy-Preserving Calibration via Statistical Modeling on Probability Simplex](https://mlsanity.com/paper/2402.13765/) (2024)
- [Understanding the Dependence of Perception Model Competency on Regions in an Image](https://mlsanity.com/paper/2407.10543/) (2024)
- [Automated Real-time Assessment of Intracranial Hemorrhage Detection AI Using an Ensembled Monitoring Model (EMM)](https://mlsanity.com/paper/2505.11738/) (2025)
- [Mimir: Hierarchical Goal-Driven Diffusion with Uncertainty Propagation for End-to-End Autonomous Driving](https://mlsanity.com/paper/2512.07130/) (2025)
- [Generalized Uncertainty of Deep Neural Networks: Taxonomy and Applications](https://mlsanity.com/paper/2302.01440/) (2023)
- [Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimates](https://mlsanity.com/paper/2303.08587/) (2023)
- [Quantifying Uncertainty in the Presence of Distribution Shifts](https://mlsanity.com/paper/2506.18283/) (2025)
- [Towards Reliable Time Series Forecasting under Future Uncertainty: Ambiguity and Novelty Rejection Mechanisms](https://mlsanity.com/paper/2503.19656/) (2025)
- [Graceful Degradation and Related Fields](https://mlsanity.com/paper/2106.11119/) (2021)
- [Efficient IoT Inference via Context-Awareness](https://mlsanity.com/paper/2310.19112/) (2023)
- [Expert-aware uncertainty estimation for quality control of neural-based blood typing](https://mlsanity.com/paper/2407.11181/) (2024)
- [A Framework for Uncertainty Quantification Based on Nearest Neighbors Across Layers](https://mlsanity.com/paper/2506.19895/) (2025)
- [A Machine Learning Perspective on Automated Driving Corner Cases](https://mlsanity.com/paper/2510.10653/) (2025)
- [Revisiting Neural Activation Coverage for Uncertainty Estimation](https://mlsanity.com/paper/2604.22360/) (2026)

## Abstract (arXiv)

Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate prediction uncertainty in a pre-trained neural network model. Our method estimates the training data density in representation space for a novel input. A neural network model then uses this information to determine whether we expect the pre-trained model to make a correct prediction. This uncertainty model is trained by predicting in-distribution errors, but can detect out-of-distribution data without having seen any such example. We test our method for a state-of-the art image classification model in the settings of both in-distribution uncertainty estimation as well as out-of-distribution detection.