# Extremal graphical modeling with latent variables via convex optimization

arXiv: https://arxiv.org/abs/2403.09604 · HTML: https://mlsanity.com/paper/2403.09604/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Builds on (most cited first, 13 of 13)

- [Sparse Structures for Multivariate Extremes](https://mlsanity.com/paper/2004.12182/) (2020)
- [Extremes on river networks](https://mlsanity.com/paper/1501.02663/) (2015)
- [Exact simulation of max-stable processes](https://mlsanity.com/paper/1506.04430/) (2015)
- [Structure learning for extremal tree models](https://mlsanity.com/paper/2012.06179/) (2020)
- [Statistical Inference for H"usler-Reiss Graphical Models Through Matrix Completions](https://mlsanity.com/paper/2210.14292/) (2022)
- [Graphical models for infinite measures with applications to extremes](https://mlsanity.com/paper/2211.15769/) (2022)
- [Extremes in High Dimensions: Methods and Scalable Algorithms](https://mlsanity.com/paper/2303.04258/) (2023)
- [Interpreting Latent Variables in Factor Models via Convex Optimization](https://mlsanity.com/paper/1601.00389/) (2016)
- [Subbotin Graphical Models for Extreme Value Dependencies with Applications to Functional Neuronal Connectivity](https://mlsanity.com/paper/2106.11554/) (2021)
- [Graphical lasso for extremes](https://mlsanity.com/paper/2307.15004/) (2023)
- [Graphical models for multivariate extremes](https://mlsanity.com/paper/2402.02187/) (2024)
- [Modelling multivariate extreme value distributions via Markov trees](https://mlsanity.com/paper/2208.02627/) (2022)
- [Parametric and nonparametric symmetries in graphical models for extremes](https://mlsanity.com/paper/2306.00703/) (2023)

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

- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)

## Abstract (arXiv)

Extremal graphical models encode the conditional independence structure of multivariate extremes and provide a powerful tool for quantifying the risk of rare events. Prior work on learning these graphs from data has focused on the setting where all relevant variables are observed. For the popular class of H"usler-Reiss models, we propose the texttteglatent method, a tractable convex program for learning extremal graphical models in the presence of latent variables. Our approach decomposes the H"usler-Reiss precision matrix into a sparse component encoding the graphical structure among the observed variables after conditioning on the latent variables, and a low-rank component encoding the effect of a few latent variables on the observed variables. We provide finite-sample guarantees of texttteglatent and show that it consistently recovers the conditional graph as well as the number of latent variables. We highlight the improved performances of our approach on synthetic and real data.