# Robust Statistical Scaling of Outlier Scores: Improving the Quality of Outlier Probabilities for Outliers (Extended Version)

arXiv: https://arxiv.org/abs/2408.15874 · HTML: https://mlsanity.com/paper/2408.15874/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 42 references that are in the map.
- First posted on arXiv 28 Aug 2024.

## Builds on (most cited first, 5 of 5)

- [PyOD: A Python Toolbox for Scalable Outlier Detection](https://mlsanity.com/paper/1901.01588/) (2019)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [Toward Unsupervised Outlier Model Selection](https://mlsanity.com/paper/2211.01834/) (2022)
- [Sequential Ensemble Learning for Outlier Detection: A Bias-Variance Perspective](https://mlsanity.com/paper/1609.05528/) (2016)

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

- [The Impact of Feature Scaling In Machine Learning: Effects on Regression and Classification Tasks](https://mlsanity.com/paper/2506.08274/) (2025)

## Abstract (arXiv)

Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be difficult for humans to interpret. Statistical scaling addresses this problem by transforming outlier scores into outlier probabilities without using ground-truth labels, thereby improving interpretability and comparability across algorithms. However, the quality of this transformation can be different for outliers and inliers. Missing outliers in scenarios where they are of particular interest - such as healthcare, finance, or engineering - can be costly or dangerous. Thus, ensuring good probabilities for outliers is essential. This paper argues that statistical scaling, as commonly used in the literature, does not produce equally good probabilities for outliers as for inliers. Therefore, we propose robust statistical scaling, which uses robust estimators to improve the probabilities for outliers. We evaluate several variants of our method against other outlier score transformations for real-world datasets and outlier detection algorithms, where it can improve the probabilities for outliers.