Vine copula mixture models and clustering for non-Gaussian data

Şahin, Özge Uysal; Czado, Claudia

doi:10.1016/j.ecosta.2021.08.011

“…Comparing the result of the Fvcmm and GMM algorithm for the Sonar data set, BIC criterion selects the Fvcmm model, while its www.nature.com/scientificreports/ accuracy classification is lower than that of the GMM model. Therefore, our findings support the one of 7 , that a better selection criterion than BIC value is needed for the vine copula model, which can be considered as possible future work. • If the data exhibit a strong conditional dependency structure, with a truncation tree level that can vary from one cluster to another, then the performance of the Tvcmm is superior to other fitted models.…”

Section: Discussionsupporting

confidence: 83%

“…To illustrate the performance of the proposed method, we apply it to a simulation and real data sets. We evaluate the performance of the newly proposed method (Tvcmm), the Fcvmm algorithm of 7 , the Gaussian mixture model (GMM), and k-means. Figure 2 shows the Box plots of the misclassification rate of each algorithm per simulation replication data set.…”

Section: Discussionmentioning

confidence: 99%

Novel pruning and truncating of the mixture of vine copula clustering models

Alanazi

¹

2022

Sci Rep

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The mixture of the vine copula densities allows selecting the vine structure, the most appropriate type of parametric marginal distributions, and the pair-copulas individually for each cluster. Therefore, complex hidden dependence structures can be fully uncovered and captured by the mixture of vine copula models without restriction to the parametric shape of margins or dependency patterns. However, this flexibility comes with the cost of dramatic increases in the number of model parameters as the dimension increases. Pruning and truncating each cluster of the mixture model will dramatically reduce the number of model parameters. This paper, therefore, introduced the first pruning and truncating techniques for the model-based clustering algorithm using the vine copula model, providing a significant contribution to the state-of-the-art. We apply the proposed methods to a number of well-known data sets with different dimensions. The results show that the performance of the individual pruning and truncation for each model cluster is superior to an existing vine copula clustering model.

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“…To illustrate the performance of the proposed method, we apply it to a simulation and real data sets. For the comparison reason, we compare the proposed model with the one of the 7 . For the simulation study, the misclassification rate of the T-vcmm model is better than that of the F-vcmm.…”

Section: Discussionmentioning

confidence: 99%

“…This section will briefly introduce the model-based clustering algorithm with the vine copula model using the ECM algorithm following the work of 7 . For more details, we refer to the latter reference.…”

Section: Finite Mixture With Vine Copula Modelmentioning

confidence: 99%

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Novel pruning and truncating of the mixture of vine copula clustering models

Alanazi

¹

2022

Preprint

0

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The mixture of the vine copula densities allows selecting the vine structure, the most appropriate type of parametric marginal distributions, and the pair-copulas individually for each cluster. Therefore, complex hidden dependence structures can be fully uncovered and captured by the mixture of vine copula models without restriction to the parametric shape of margins or dependency patterns. However, this flexibility comes with the cost of dramatic increases in the number of model parameters as the dimension increases. Pruning and truncating each cluster of the mixture model will dramatically reduce the number of model parameters. This paper, therefore, introduced the first pruning and truncating techniques for the model-based clustering algorithm using the vine copula model, providing a significant contribution to the state-of-the-art. We apply the proposed methods to a number of well-known data sets with different dimensions. The results show that the performance of the individual pruning and truncation for each model cluster is superior to an existing vine copula clustering model.

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D‐vine‐copula‐based postprocessing of wind speed ensemble forecasts

Jobst

¹

,

Möller

²

,

Groß

³

2023

Quart J Royal Meteoro Soc

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Current practice in predicting future weather is the use of numerical weather prediction (NWP) models to produce ensemble forecasts. Despite of enormous improvements over the last few decades, they still tend to exhibit bias and dispersion errors and, consequently, lack calibration. Therefore, these forecasts may be improved by statistical postprocessing. In this work, we propose a D‐vine‐copula‐based postprocessing for 10 m surface wind speed ensemble forecasts. This approach makes use of quantile regression related to D‐vine copulas, which is highly data driven and allows one to adopt more general dependence structures as the state‐of‐the‐art zero‐truncated ensemble model output statistic (tEMOS) model. We compare local and global D‐vine copula quantile regression (DVQR) models to the corresponding tEMOS models and their gradient‐boosting extensions (tEMOS‐GB) for different sets of predictor variables using one lead time and 60 surface weather stations in Germany. Furthermore, we investigate which types of training periods can improve the performance of tEMOS and the D‐vine‐copula‐based method for wind speed postprocessing. We observe that the D‐vine‐based postprocessing yields a comparable performance with respect to tEMOS if only wind speed ensemble variables are included and to substantial refinements if additional meteorological and station‐specific weather variables are integrated. As our main result, we note that, in the global setting, DVQR is able to provide better scores than tEMOS‐GB in general, whereas the local DVQR is able to substantially outperform the local tEMOS‐GB at particular stations admitting nonlinear relationships among the variables. In addition, we remark that training periods capturing seasonal patterns perform the best. Last but not least, we adapt a criterion for calculating the variable importance in D‐vine copulas and we outline which predictor variables are due to this approach the most important for the correction of wind speed ensemble forecasts.

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Vine copula mixture models and clustering for non-Gaussian data

Cited by 12 publications

References 47 publications

Novel pruning and truncating of the mixture of vine copula clustering models

Novel pruning and truncating of the mixture of vine copula clustering models

Novel pruning and truncating of the mixture of vine copula clustering models

D‐vine‐copula‐based postprocessing of wind speed ensemble forecasts

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