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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.

Keywords

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}
}
R2 v1 2026-06-28T13:42:17.110Z