图的最大似然阈值
The Maximum Likelihood Threshold of a Graph
摘要：
图的最大似然阈值是保证最大似然估计几乎肯定存在于与图相关联的高斯图模型中的最小数据点数量。我们表明，这个图形参数是连接到组合刚性理论。特别地，如果图$G$的边集是$n-1$维通用刚性拟阵中的独立集，则$G$的最大似然阈值小于或等于$n$。这种联系使我们能够证明关于最大似然阈值的许多结果。
英文摘要：
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph parameter is connected to the theory of combinatorial rigidity. In particular, if the edge set of a graph $G$ is an independent set in the $n-1$-dimensional generic rigidity matroid, then the maximum likelihood threshold of $G$ is less than or equal to $n$. This connection allows us to prove many results about the maximum likelihood threshold.
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