# Trunc-Opt vine building algorithms

arXiv: https://arxiv.org/abs/2512.14399 · HTML: https://mlsanity.com/paper/2512.14399/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 4 of 4)

- [Nonparametric estimation of simplified vine copula models: comparison of methods](https://mlsanity.com/paper/1701.00845/) (2017)
- [Model selection in sparse high-dimensional vine copula models with application to portfolio risk](https://mlsanity.com/paper/1801.09739/) (2018)
- [Hypergraphs in the characterization of regular vine copula structures](https://mlsanity.com/paper/1604.02652/) (2016)
- [On the connection between cherry-tree copulas and truncated R-vine copulas](https://mlsanity.com/paper/1604.03269/) (2016)

## Built on by (most cited first, 1 of 1)

- [Bayesian model selection of vine copulas: a loss-based perspective](https://mlsanity.com/paper/2606.21512/) (2026)

## Abstract (arXiv)

Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the random variables involved. However, their flexibility comes with the drawback of a high-dimensional parameter space. To tackle this problem, truncated vine copulas were introduced by Kurowicka (2010) (Gaussian case) and Brechmann and Czado (2013) (general case). Truncated vine copulas contain conditionally independent pair copulas after the truncation level. So far, in the general case, truncated vine constructing algorithms started from the lowest tree in order to encode the largest dependences in the lower trees. The novelty of this paper starts from the observation that a truncated vine is determined by the first tree after the truncation level (see Kov'acs and Sz'antai (2017)). This paper introduces a new score for fitting truncated vines to given data, called the Weight of the truncated vine. Then we propose a completely new methodology for constructing truncated vines. We prove theorems which motivate this new approach. While earlier algorithms did not use conditional independences, we give algorithms for constructing and encoding truncated vines which do exploit them. Finally, we illustrate the algorithms on real datasets and compare the results with well-known methods included in R packages. Our method generally compare favorably to previously known methods.