# Maximum likelihood thresholds of Gaussian graphical models and graphical lasso

arXiv: https://arxiv.org/abs/2312.03145 · HTML: https://mlsanity.com/paper/2312.03145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 14 references that are in the map.
- First posted on arXiv 5 Dec 2023.

## Builds on (most cited first, 1 of 1)

- [On the inconsistency of ℓ1-penalised sparse precision matrix estimation](https://mlsanity.com/paper/1603.02532/) (2016)

## Abstract (arXiv)

Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likelihood threshold of a graph is the minimum number of data points required to fit the corresponding graphical model using maximum likelihood estimation. Graphical lasso is a method for selecting and fitting a graphical model. In this project, we ask: when graphical lasso is used to select and fit a graphical model on n data points, how likely is it that n is greater than or equal to the maximum likelihood threshold of the corresponding graph? Our results are a series of computational experiments.