Maximum likelihood thresholds of Gaussian graphical models and graphical lasso
Statistics Theory
2023-12-07 v1 Machine Learning
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2312.03145,
title = {Maximum likelihood thresholds of Gaussian graphical models and graphical lasso},
author = {Daniel Irving Bernstein and Hayden Outlaw},
journal= {arXiv preprint arXiv:2312.03145},
year = {2023}
}