Computing maximum likelihood thresholds using graph rigidity

Daniel Irving Bernstein, Sean Dewar, Steven J. Gortler, Anthony Nixon, Meera Sitharam, Louis Theran

Research output: Working paperPreprint

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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.
Original languageEnglish
PublisherarXiv.org
DOIs
Publication statusPublished - 20 Oct 2022

Bibliographical note

15 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2108.02185

Keywords

  • math.CO
  • math.MG
  • math.ST
  • stat.TH
  • 62H12 (Primary), 52C25 (Secondary)

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