Localized Anomaly Detection via Differentiable D-vine Copulas

2026-07-27

AI Summary

This work addresses the limitations of traditional D-vine copula fitting, which relies on greedy strategies prone to local optima and lacks support for interpretable local anomaly detection. The authors propose the first fully differentiable D-vine copula fitting framework, integrating beam search with gradient-based optimization to enhance global fit quality through multi-path exploration. Leveraging the hierarchical dependency structure inherent in D-vines, the method enables edge-level anomaly localization alongside global anomaly scoring. Furthermore, it incorporates Mondrian conformal prediction to provide statistically valid uncertainty quantification for local anomalies. Experimental results demonstrate that the proposed approach significantly outperforms existing methods across multiple benchmark and real-world datasets, achieving superior performance in both interpretability and anomaly detection accuracy.

Abstract

Vine copulas provide a flexible framework for modeling complex multivariate distributions through a hierarchical decomposition into bivariate pair-copulas. Fitting a D-vine requires selecting a copula family and parameter configuration for each pair-copula from a set of candidates encoding different dependence patterns. As the number of variables and candidate families increases, the number of possible configurations grows combinatorially. Existing fitting procedures address this challenge through sequential greedy decisions, committing to a single locally optimal family at each step and potentially discarding configurations that would yield a better global fit. To overcome this limitation, we propose a novel estimation framework that combines gradient-based maximum likelihood estimation, enabled by our fully differentiable implementation, with a beam-search strategy that maintains multiple competing D-vine configurations throughout the fitting process. This allows a broader exploration of the configuration space while remaining computationally tractable. Building on the fitted D-vine, we introduce a localized anomaly detection framework that exploits the hierarchical decomposition to produce both global anomaly scores and edge-level explanations. Statistical guarantees are provided through Mondrian conformal prediction, while the pair-copula structure enables the localization of anomalies to specific variable relationships. We evaluate the proposed framework on both benchmark and real-world datasets, demonstrating its effectiveness for interpretable anomaly detection with uncertainty quantification.

Problem

• D-vine copulas
• anomaly detection
• model selection
• combinatorial optimization
• localization

Innovation

• Differentiable D-vine Copulas
• Beam Search
• Localized Anomaly Detection
• Conformal Prediction
• Hierarchical Dependence Modeling