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.

翻译：每个图G对应一个高斯图模型。这类模型常用于高维场景，即变量数量较多而数据点相对较少的情况。图的极大似然阈值是指通过极大似然估计拟合对应图模型所需的最小数据点数。图套索（graphical lasso）是一种图模型选择与拟合方法。本研究提出以下问题：当使用图套索对n个数据点进行图模型选择与拟合时，n大于或等于对应图极大似然阈值的概率有多大？我们的研究结果基于一系列计算实验。