通过可微 D-vine 相依函数进行局部异常检测
Localized Anomaly Detection via Differentiable D-vine Copulas
- University of Trieste（的里雅斯特大学）
- Idrostudi srl（伊德罗斯图迪有限公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究通过可微 D-vine 相依函数进行局部异常检测，提出结合梯度最大似然估计与波束搜索策略的框架拟合 D-vine，在此基础上引入局部异常检测框架，在多数据集评估，能有效进行可解释异常检测并量化不确定性。
AI中文摘要：
Vine 相依函数为通过分层分解为二元配对相依函数来建模复杂多元分布提供了一个灵活框架。拟合 D-vine 需要从一组编码不同相依模式的候选函数中为每个配对相依函数选择一个相依函数族和参数配置。随着变量数量和候选族数量增加，可能配置数量呈组合增长。现有拟合程序通过顺序贪婪决策应对这一挑战，在每一步致力于单个局部最优族，可能丢弃能产生更好全局拟合的配置。为克服此限制，我们提出一种新颖估计框架，将基于梯度的最大似然估计（通过我们的全可微实现实现）与波束搜索策略相结合，在整个拟合过程中维持多个相互竞争的 D-vine 配置。这允许在计算上易于处理的同时更广泛地探索配置空间。基于拟合的 D-vine，我们引入一个局部异常检测框架，利用分层分解产生全局异常分数和边缘级解释。通过蒙德里安共形预测提供统计保证，而配对相依函数结构使异常能够定位到特定变量关系。我们在基准和真实世界数据集上评估所提出框架，证明其在具有不确定性量化的可解释异常检测方面的有效性。
英文摘要：
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.
