Statistical learning with vine copulas

• Applicant: Professorin Dr. Claudia Czado
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing ; Mathematics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 414226540

• Final Report Year: 2024

Final Report Abstract

Statistical learning methods for data on many variables have not only to adequately model each variable’s behavior separately but also allow for dependence between them. The copula approach is highly suitable since it builds models by joining separate marginal models with a copula describing the dependence. A stumbling block for the application of such copula-based models in statistical learning problems was the lack of flexible copula models in high dimensions. Vine copulas have recently been shown to be suitable to handle asymmetric tail dependence. These are observed in risk management in finance, insurance, engineering and environmental science. Standard dependence models such as the multivariate Gaussian or Student t distribution cannot accommodate asymmetric tails. Vine copula-based models can be used in high dimensions since they are constructed with the help of independent bivariate copula blocks. This project harvests these advantages to build and implement a copula-based statistical learning toolbox for challenging high-dimensional applications. In particular, the estimation and selection of new vine-based quantile regression methods have been investigated. Further clustering and classification tasks were approached by designing novel mixture models with vine components. Statistical theory to allow for uncertainty assessment of prediction of conditional quantiles as well as of out-of-sample cluster and classification assignments has been developed. The advantages of these more realistic and flexible modeling approaches have been demonstrated through comparison studies.

Publications

• Bivariate vine copula based regression, bivariate level and quantile curves
  Tepegjozova, M. & Czado, C.
  
• Nonparametric C- and D-vine-based quantile regression. Dependence Modeling, 10(1), 1-21.
  Tepegjozova, Marija; Zhou, Jing; Claeskens, Gerda & Czado, Claudia
  
• Predicting times to event based on vine copula models. Computational Statistics & Data Analysis, 175, 107546.
  Pan, Shenyi & Joe, Harry
  
• Vine copula mixture models and clustering for non-Gaussian data. Econometrics and Statistics, 22, 136-158.
  Sahin, Özge & Czado, Claudia
  
• Assessing univariate and bivariate risks of late-frost and drought using vine copulas: A historical study for Bavaria
  Tepegjozova, M., Meyer, B. F., Rammig, A., Zang, C. S. & Czado, C.
  
• Conditional inferences and predictions based on copula models. (Ph.D. thesis). University of British Columbia
  Pan, S.
  
• Statistical learning based on vine copulas with societal applications (Ph.D. thesis). Technische Universität München
  Sahin, Ö.
  
• Statistical learning with vine copulas in regression settings (Ph.D. thesis). Technische Universität München
  Tepegjozova, M.
  
• Assessing copula models for mixed continuous-ordinal variables. Dependence Modeling, 12(1).
  Pan, Shenyi & Joe, Harry
  
• High-dimensional sparse vine copula regression with application to genomic prediction. Biometrics, 80(1).
  Sahin, Özge & Czado, Claudia
  
• Vine Copula-Based Classifiers with Applications. Journal of Classification, 42(2), 335-363.
  Şahin, Özge & Joe, Harry