Maximum likelihood thresholds of Gaussian graphical models and graphical lasso

Daniel Irving Bernstein; Hayden Outlaw

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arXiv · 2312.03145

Maximum likelihood thresholds of Gaussian graphical models and graphical lasso

Daniel Irving Bernstein·Hayden Outlaw

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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.

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Daniel Irving Bernstein, Hayden Outlaw. 2023-12-05. Maximum likelihood thresholds of Gaussian graphical models and graphical lasso. https://arxiv.org/abs/2312.03145

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