# On the use of Mahalanobis distance for out-of-distribution detection with neural networks for medical imaging

arXiv: https://arxiv.org/abs/2309.01488 · HTML: https://mlsanity.com/paper/2309.01488/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 33 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Builds on (most cited first, 26 of 26)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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 Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection](https://mlsanity.com/paper/2106.09022/) (2021)
- [DICE: Leveraging Sparsification for Out-of-Distribution Detection](https://mlsanity.com/paper/2111.09805/) (2021)
- [Autoencoders for Unsupervised Anomaly Segmentation in Brain MR Images: A Comparative Study](https://mlsanity.com/paper/2004.03271/) (2020)
- [Denoising diffusion models for out-of-distribution detection](https://mlsanity.com/paper/2211.07740/) (2022)
- [Unsupervised domain adaptation for medical imaging segmentation with self-ensembling](https://mlsanity.com/paper/1811.06042/) (2018)
- [Unknown-Aware Object Detection: Learning What You Don't Know from Videos in the Wild](https://mlsanity.com/paper/2203.03800/) (2022)
- [Does Your Dermatology Classifier Know What It Doesn't Know? Detecting the Long-Tail of Unseen Conditions](https://mlsanity.com/paper/2104.03829/) (2021)
- [RankFeat: Rank-1 Feature Removal for Out-of-distribution Detection](https://mlsanity.com/paper/2209.08590/) (2022)
- [Detecting Outliers with Foreign Patch Interpolation](https://mlsanity.com/paper/2011.04197/) (2020)
- [Confidence-based Out-of-Distribution Detection: A Comparative Study and Analysis](https://mlsanity.com/paper/2107.02568/) (2021)
- [Why is the Mahalanobis Distance Effective for Anomaly Detection?](https://mlsanity.com/paper/2003.00402/) (2020)
- [The challenges of deploying artificial intelligence models in a rapidly evolving pandemic](https://mlsanity.com/paper/2005.12137/) (2020)
- [Out of Distribution Detection and Adversarial Attacks on Deep Neural Networks for Robust Medical Image Analysis](https://mlsanity.com/paper/2107.04882/) (2021)
- [FRODO: Free rejection of out-of-distribution samples: application to chest x-ray analysis](https://mlsanity.com/paper/1907.01253/) (2019)
- [Generating Artificial Outliers in the Absence of Genuine Ones -- a Survey](https://mlsanity.com/paper/2006.03646/) (2020)

## Built on by (most cited first, 15 of 15)

- [Mahalanobis++: Improving OOD Detection via Feature Normalization](https://mlsanity.com/paper/2505.18032/) (2025)
- [Robust Conformal Volume Estimation in 3D Medical Images](https://mlsanity.com/paper/2407.19938/) (2024)
- [COMPASS: Robust Feature Conformal Prediction for Medical Segmentation Metrics](https://mlsanity.com/paper/2509.22240/) (2025)
- [Deciphering the Definition of Adversarial Robustness for post-hoc OOD Detectors](https://mlsanity.com/paper/2406.15104/) (2024)
- [Evaluating Reliability in Medical DNNs: A Critical Analysis of Feature and Confidence-Based OOD Detection](https://mlsanity.com/paper/2408.17337/) (2024)
- [Subgroups Matter for Robust Bias Mitigation](https://mlsanity.com/paper/2505.21363/) (2025)
- [Robustness Testing of Black-Box Models Against CT Degradation Through Test-Time Augmentation](https://mlsanity.com/paper/2406.19557/) (2024)
- [Dimensionality Reduction and Nearest Neighbors for Improving Out-of-Distribution Detection in Medical Image Segmentation](https://mlsanity.com/paper/2408.02761/) (2024)
- [DIsoN: Decentralized Isolation Networks for Out-of-Distribution Detection in Medical Imaging](https://mlsanity.com/paper/2506.09024/) (2025)
- [Confidence-Uncertainty Boundary Calibration for Bayesian Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/2602.11973/) (2026)
- [The Invisible Gorilla Effect in Out-of-distribution Detection](https://mlsanity.com/paper/2602.20068/) (2026)
- [MM++: Post-Hoc Scale-Invariant Multilayer OOD Detection via Top-K Gated Feature Fusion](https://mlsanity.com/paper/2606.17352/) (2026)
- [MaRS: Robust Out-of-Distribution Detection via Mahalanobis Residual Scoring](https://mlsanity.com/paper/2606.22649/) (2026)
- [Unified Multi-Layer Subspace Modeling for Cross-Domain OOD Detection](https://mlsanity.com/paper/2609.06785/) (2026)
- [Mitigating Shortcut Learning: Texture-Penalized Prototype Networks](https://mlsanity.com/paper/2609.07504/) (2026)

## Abstract (arXiv)

Implementing neural networks for clinical use in medical applications necessitates the ability for the network to detect when input data differs significantly from the training data, with the aim of preventing unreliable predictions. The community has developed several methods for out-of-distribution (OOD) detection, within which distance-based approaches - such as Mahalanobis distance - have shown potential. This paper challenges the prevailing community understanding that there is an optimal layer, or combination of layers, of a neural network for applying Mahalanobis distance for detection of any OOD pattern. Using synthetic artefacts to emulate OOD patterns, this paper shows the optimum layer to apply Mahalanobis distance changes with the type of OOD pattern, showing there is no one-fits-all solution. This paper also shows that separating this OOD detector into multiple detectors at different depths of the network can enhance the robustness for detecting different OOD patterns. These insights were validated on real-world OOD tasks, training models on CheXpert chest X-rays with no support devices, then using scans with unseen pacemakers (we manually labelled 50% of CheXpert for this research) and unseen sex as OOD cases. The results inform best-practices for the use of Mahalanobis distance for OOD detection. The manually annotated pacemaker labels and the project's code are available at: https://github.com/HarryAnthony/Mahalanobis-OOD-detection.