A computational approach to maximum likelihood thresholds for colored Gaussian graphical models

The paper presents a computational framework for determining the maximum likelihood threshold (MLT) in colored Gaussian graphical models (CGGMs). It focuses on a geometric approach that seeks the minimal rank of a sample covariance matrix whose projection lies within the interior of the cone of sufficient statistics. The authors extend theoretical results from uncolored to colored models, introduce new symbolic algorithms, and demonstrate how topological data analysis (TDA) can alleviate computational challenges associated with traditional symbolic algebraic methods.

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