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Computing maximum likelihood thresholds using graph rigidity

Year: 2023
Type: article
Abstract: 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.
DOI: 10.2140/astat.2023.14.287
Authors: Daniel Irving Bernstein, Sean Dewar, Steven J. Gortler, Anthony Nixon, Meera Sitharam, Louis Theran
Institutions: Tulane University, University of Bristol, Harvard University, Lancaster University, University of Florida, University of St Andrews
Language: English
Open Access status: diamond
Awards: The graph rigidity problem in arbitrary dimension, Realizations of Rigid Graphs, G257083437, FRG: Collaborative Research: Stability of Structures Large and Small, Collaborative Research: Geometric Elucidation of Supramolecular Assembly and Allostery with Experimental Validation, FRG: Collaborative Research: Stability of Structures Large and Small, G6366385795, G7501454329, G7852429223, PostDoctoral Research Fellowship, G8154314218, G829238173
OpenAlex ID: W4396965671
FWCI: 0.262
Cites: 17
Cited by: 3
Related to: 10