# Matrix and graph representations of vine copula structures

arXiv: https://arxiv.org/abs/2205.04783 · HTML: https://mlsanity.com/paper/2205.04783/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 10 May 2022.

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

- [Copula-based anomaly scoring and localization for large-scale, high-dimensional continuous data](https://mlsanity.com/paper/1912.02166/) (2019)
- [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)
- [A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence](https://mlsanity.com/paper/1506.03920/) (2015)

## Abstract (arXiv)

Vine copulas can efficiently model multivariate probability distributions. This paper focuses on a more thorough understanding of their structures, since in the literature, vine copula representations are often ambiguous. The graph representations include the original, cherry and chordal graph sequence structures, which we show equivalence between. Importantly we also show a new result, namely that when a perfect elimination ordering of a vine structure is given, then it can always be uniquely represented with a matrix. O. M. N'apoles has shown a way to represent vines in a matrix, and we algorithmify this previous approach, while also showing a new method for constructing such a matrix, through cherry tree sequences. We also calculate the runtime of these algorithms. Lastly, we prove that these two matrix-building algorithms are equivalent if the same perfect elimination ordering is being used.