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

Computing maximum likelihood thresholds using graph rigidity