Decoupling Dependency Structures: Sklar’s theorem for explainable outlier detection

Philipp Haid, Julian Wustl, Yarema Okhrin, Claudius Schnörr

Keywords: Outlier Detection, Explainability, Copula Modeling

TL;DR: We present a highly explainable, copula-based outlier detector.

Abstract: Recent advances in outlier detection have been primarily driven by deep learning models, which, while powerful, have substantial drawbacks in terms of explainability. This is particularly relevant in fields that demand detailed reasoning and understanding of why observations are classified as outliers. To close the gap between state-of-the-art performance and enhanced explainability, we propose Vine Copula-Based Outlier Detection (VC-BOD). We utilize Sklar’s theorem in conjunction with vine copulas and univariate kernel density estimators to decouple marginal distributions and their dependency structure for outlier detection. Our model uses a closed-form equation for the outlier score, which allows for detailed explainability and feature attribution. VC-BOD employs a traceable criterion to determine whether a new observation is an outlier, while also identifying the specific features responsible for this classification. The proposed model further distinguishes whether these features deviate from their own distributions or from interactions with other features. Our empirical evaluations demonstrate that VC-BOD outperforms most benchmarked classical models and several deep learning approaches in terms of average rank performance while proving competitive with the best-performing models.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 7182