论文标题
特征聚类用于极端区域的支持识别
Feature Clustering for Support Identification in Extreme Regions
论文作者
论文摘要
了解多元极端的复杂结构是从投资组合监控和环境风险管理到保险的各个领域的主要挑战。在多元极端价值理论的框架中，极端依赖性结构的共同表征是角度度量。它是在极端地区工作的合适措施，因为它提供了有关极端倾向于集中质量的子区域的有意义的见解。本文开发了一种基于优化的新方法来评估极端的依赖性结构。此支持标识方案将重写为估计最能捕获极端支撑的特征簇。我们提供的降低技术应用于统计学习任务，例如特征聚类和异常检测。数值实验为我们方法的相关性提供了有力的经验证据。
Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common characterization of extremes' dependence structure is the angular measure. It is a suitable measure to work in extreme regions as it provides meaningful insights concerning the subregions where extremes tend to concentrate their mass. The present paper develops a novel optimization-based approach to assess the dependence structure of extremes. This support identification scheme rewrites as estimating clusters of features which best capture the support of extremes. The dimension reduction technique we provide is applied to statistical learning tasks such as feature clustering and anomaly detection. Numerical experiments provide strong empirical evidence of the relevance of our approach.
