Home > Research > Publications & Outputs > Computing maximum likelihood thresholds using g...

Electronic data

  • MLTs_Small_graphs-accepted

    Accepted author manuscript, 446 KB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

Links

Text available via DOI:

View graph of relations

Computing maximum likelihood thresholds using graph rigidity

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
  • Daniel Bernstein
  • Sean Dewar
  • Steven Gortler
  • Anthony Nixon
  • Meera Sitharam
  • Louis Theran
Close
<mark>Journal publication date</mark>31/12/2023
<mark>Journal</mark>Algebraic Statistics
Issue number2
Volume14
Number of pages19
Pages (from-to)287-305
Publication StatusPublished
<mark>Original language</mark>English

Abstract


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. We recently proved a new characterization of the MLT in terms of rigidity-theoretic properties of
G
. 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 nine vertices, graphs with at most 24 edges, every graph sufficiently close to a complete graph and graphs with bounded degrees.