Differentiable D-vine Copulas Enable Localized, Interpretable Anomaly Detection

Modeling complex multivariate distributions is crucial for effective anomaly detection, and vine copulas offer a flexible framework for this by decomposing distributions into a hierarchy of bivariate pair-copulas. However, fitting D-vine copulas traditionally involves sequential greedy decisions, which can lead to suboptimal global fits by committing to a single local optimum at each step. This new research introduces an innovative estimation framework to overcome this limitation. The proposed framework combines gradient-based maximum likelihood estimation, enabled by a fully differentiable implementation of D-vine copulas, with a beam-search strategy. This approach allows the system to maintain and explore multiple competing D-vine configurations throughout the fitting process, significantly broadening the search space while remaining computationally tractable. This ensures a more globally optimal model fit. Building on these fitted D-vine copulas, the researchers developed a localized anomaly detection framework. This system leverages the hierarchical decomposition to generate not only global anomaly scores but also detailed, edge-level explanations that pinpoint specific variable relationships contributing to an anomaly. Statistical guarantees are provided through Mondrian conformal prediction, offering robust uncertainty quantification. Evaluations on benchmark and real-world datasets confirm the framework's effectiveness for interpretable anomaly detection.