Vine copulas provide a flexible framework for modeling complex multivariate distributions through 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, resulting in combinatorial growth as the number of variables and candidate families increases. Existing fitting procedures tackle this challenge with sequential greedy decisions, committing to a single locally optimal family at each step, potentially discarding configurations that could 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 for a broader exploration of the configuration space while remaining computationally feasible.
Building on the fitted D-vine, we introduce a localized anomaly detection framework that leverages 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.
Blogger's Review: The proposed localized anomaly detection framework effectively enhances the interpretability and accuracy of anomaly detection by integrating differentiable D-vine copulas with a beam search strategy. Its innovative statistical guarantees provide robust support for practical applications, showcasing promising prospects in high-dimensional data environments.