Statistical learning with vine copulas

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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.