Statistical learning with vine copulas

使用 vine copula 进行统计学习

• 批准号: 414226540
• 负责人: Professorin Dr. Claudia Czado
• 金额: --
• 依托单位: Lehrstuhl für Mathematische Statistik (M4)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/414226540?language=en
• 关键词: Statistical; learning; vine; copulas

Statistical learning methods for data on many variables have to not only adequately model the behavior of each variable separately but also to allow for dependence between them. The copula approach is highly suitable since it builds models by joining separate marginal functions with a copula describing the dependence. An obstacle for the application of such copula based models in statistical learning was their lack of flexibility in high dimensions. The class of vine copulas however has recently shown to be suitable for dependence modeling in high dimensions, since they are constructed with the help of independent bivariate copula blocks. Further vine copula based models can capture asymmetric tail dependence. These are observed in risk management in finance, insurance and engineering. Standard dependence models such as the multivariate Gaussian or Student t distribution cannot accommodate asymmetric tails. This project wants to harvest these advantages to build and implement a vine copula based statistical learning toolbox for challenging high dimensional applications. In particular, we will investigate the estimation and selection of vine-based quantile regression methods. Further, we will approach clustering and classification tasks by designing novel mixture models with vine components. We will develop statistical theory to allow for uncertainty assessment of prediction of conditional quantiles as well as for the cluster and classification assignment of new data. Comparison studies will demonstrate the advantages of more realistic and interpretable modeling.

对许多变量的数据进行统计学习的方法不仅必须分别对每个变量的行为进行适当的建模，而且还必须考虑到它们之间的相关性。Copula方法非常适合，因为它通过将独立的边际函数与描述相关性的Copula相结合来建立模型。这种基于Copula的模型在统计学习中应用的一个障碍是它们在高维方面缺乏灵活性。然而，最近的研究表明，这类藤本Copula是在独立的二元Copula块的帮助下构造的，因此适合于高维的相关性建模。此外，基于Vine Copula的模型可以捕获不对称的尾部依赖关系。这些在金融、保险和工程领域的风险管理中得到了观察。标准相关性模型，如多变量高斯分布或学生t分布，不能适应非对称尾部。这个项目想要收获这些优势，以建立和实现一个基于Vine Copula的统计学习工具箱，用于挑战高维应用程序。特别是，我们将研究基于VIN的分位数回归方法的估计和选择。此外，我们将通过设计具有葡萄藤成分的新型混合模型来实现聚类和分类任务。我们将发展统计理论，以便对条件分位数的预测进行不确定性评估，以及对新数据进行分组和分类分配。比较研究将展示更真实和可解释的建模的优势。