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The maximum likelihood threshold of a graph
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The maximum likelihood threshold of a graph
The maximum likelihood threshold of a graph
Journal Article

The maximum likelihood threshold of a graph

2018
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Overview
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. We conclude by showing that these methods give exact bounds on the number of observations needed for the score matching estimator to exist with probability one.
Publisher
INTERNATIONAL STATISTICAL INSTITUTE

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