The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. Recently a new characterization of the MLT in terms of rigidity-theoretic properties of $G$ was proved \cite{Betal}. This characterization was then used to give new combinatorial lower bounds on the MLT of any graph. We continue this line of research by exploiting combinatorial rigidity results to compute the MLT precisely for several families of graphs. These include graphs with at most $9$ vertices, graphs with at most 24 edges, every graph sufficiently close to a complete graph and graphs with bounded degrees.

翻译：图形$G$的最大可能性阈值(MLT)是样本的最小数量,几乎肯定保证在相应的高斯图形模型中存在最大可能性估计值。最近,以硬度理论特性为$G$对MLT作了新的定性。然后,这种定性用于给任何图形的MLT下下一个新的组合界限。我们继续这一研究线,利用组合式刻度结果,精确计算多组图的MLT。其中包括最多为9美元的顶部图、最多为24个边缘的图、每个图都足够接近完整的图表和有界限的图表。