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

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.

Dimensionality-Aware Outlier Detection: Theoretical and Experimental Analysis

We present a nonparametric method for outlier detection that takes full account of local variations in intrinsic dimensionality within the dataset. Using the theory of Local Intrinsic Dimensionality (LID), our 'dimensionality-aware' outlier detection method, DAO, is derived as an estimator of an asymptotic local expected density ratio involving the query point and a close neighbor drawn at random. The dimensionality-aware behavior of DAO is due to its use of local estimation of LID values in a theoretically-justified way. Through comprehensive experimentation on more than 800 synthetic and real datasets, we show that DAO significantly outperforms three popular and important benchmark outlier detection methods: Local Outlier Factor (LOF), Simplified LOF, and kNN.