# Model selection in sparse high-dimensional vine copula models with application to portfolio risk

arXiv: https://arxiv.org/abs/1801.09739 · HTML: https://mlsanity.com/paper/1801.09739/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2018.

## Built on by (most cited first, 6 of 6)

- [Retrospective Uncertainties for Deep Models using Vine Copulas](https://mlsanity.com/paper/2302.12606/) (2023)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [Vine copula mixture models and clustering for non-Gaussian data](https://mlsanity.com/paper/2102.03257/) (2021)
- [Throwing Vines at the Wall: Structure Learning via Random Search](https://mlsanity.com/paper/2510.20035/) (2025)
- [Trunc-Opt vine building algorithms](https://mlsanity.com/paper/2512.14399/) (2025)
- [Bayesian model selection of vine copulas: a loss-based perspective](https://mlsanity.com/paper/2606.21512/) (2026)

## Abstract (arXiv)

Vine copulas allow to build flexible dependence models for an arbitrary number of variables using only bivariate building blocks. The number of parameters in a vine copula model increases quadratically with the dimension, which poses new challenges in high-dimensional applications. To alleviate the computational burden and risk of overfitting, we propose a modified Bayesian information criterion (BIC) tailored to sparse vine copula models. We show that the criterion can consistently distinguish between the true and alternative models under less stringent conditions than the classical BIC. The new criterion can be used to select the hyper-parameters of sparse model classes, such as truncated and thresholded vine copulas. We propose a computationally efficient implementation and illustrate the benefits of the new concepts with a case study where we model the dependence in a large stock stock portfolio.