论文标题
使用图形刚度计算最大似然阈值
Computing maximum likelihood thresholds using graph rigidity
论文作者
论文摘要
图$ g $的最大似然阈值（MLT）是几乎可以肯定地保证在相应的高斯图形模型中最大似然估计的最小样本数量。最近，证明了MLT的新特征在$ g $的刚性理论特性方面得到证明\ cite {betal}。然后使用此表征在任何图的MLT上给出新的组合下限。我们通过利用组合刚度结果来确切计算几个图族的MLT来继续进行这一研究。其中包括带有最多$ 9 $顶点的图形，最多具有24个边缘的图形，每个图都足够接近完整的图形和具有界度的图形。
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.
