# A Probabilistic Transformation of Distance-Based Outliers

arXiv: https://arxiv.org/abs/2305.09446 · HTML: https://mlsanity.com/paper/2305.09446/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 108 references that are in the map.
- First posted on arXiv 16 May 2023.

## Builds on (most cited first, 15 of 15)

- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [Interpretable Deep Learning: Interpretation, Interpretability, Trustworthiness, and Beyond](https://mlsanity.com/paper/2103.10689/) (2021)
- [Deep Nearest Neighbor Anomaly Detection](https://mlsanity.com/paper/2002.10445/) (2020)
- [LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks](https://mlsanity.com/paper/2112.05355/) (2021)
- [Explaining Anomalies in Groups with Characterizing Subspace Rules](https://mlsanity.com/paper/1708.05929/) (2017)
- [The Clever Hans Effect in Anomaly Detection](https://mlsanity.com/paper/2006.10609/) (2020)
- [Local Subspace-Based Outlier Detection using Global Neighbourhoods](https://mlsanity.com/paper/1611.00183/) (2016)
- [OutlierDetection.jl: A modular outlier detection ecosystem for the Julia programming language](https://mlsanity.com/paper/2211.04550/) (2022)

## Built on by (most cited first, 1 of 1)

- [Integration of deep generative Anomaly Detection algorithm in high-speed industrial line](https://mlsanity.com/paper/2603.07577/) (2026)

## Abstract (arXiv)

The scores of distance-based outlier detection methods are difficult to interpret, making it challenging to determine a cut-off threshold between normal and outlier data points without additional context. We describe a generic transformation of distance-based outlier scores into interpretable, probabilistic estimates. The transformation is ranking-stable and increases the contrast between normal and outlier data points. Determining distance relationships between data points is necessary to identify the nearest-neighbor relationships in the data, yet, most of the computed distances are typically discarded. We show that the distances to other data points can be used to model distance probability distributions and, subsequently, use the distributions to turn distance-based outlier scores into outlier probabilities. Our experiments show that the probabilistic transformation does not impact detection performance over numerous tabular and image benchmark datasets but results in interpretable outlier scores with increased contrast between normal and outlier samples. Our work generalizes to a wide range of distance-based outlier detection methods, and because existing distance computations are used, it adds no significant computational overhead.