# Elliptical graphical modelling

arXiv: https://arxiv.org/abs/1506.04321 · HTML: https://mlsanity.com/paper/1506.04321/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2015.

## Built on by (most cited first, 3 of 3)

- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [Nonparanormal Graph Quilting with Applications to Calcium Imaging](https://mlsanity.com/paper/2305.13491/) (2023)
- [Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning](https://mlsanity.com/paper/2506.10628/) (2025)

## Abstract (arXiv)

We propose elliptical graphical models based on conditional uncorrelatedness as a general- ization of Gaussian graphical models by letting the population distribution be elliptical instead of normal, allowing the fitting of data with arbitrarily heavy tails. We study the class of propor- tionally affine equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling, leading to a new class of partial correlation estimators and analogues of the classical deviance test. General expressions for the asymptotic variance of partial correla- tion estimators, unconstrained and under decomposable models, are given, and the asymptotic chi square approximation of the pseudo-deviance test statistic is proved. The feasibility of our approach is demonstrated by a simulation study, using, among others, Tyler's scatter estimator, which is distribution-free within the elliptical model. Our approach provides a robustification of Gaussian graphical modelling. The latter is likelihood-based and known to be very sensitive to model misspecification and outlying observations.