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

Research

Associated organisational units

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/Magazine › Journal article › peer-review

Published

Standard

Computing maximum likelihood thresholds using graph rigidity. / Bernstein, Daniel; Dewar, Sean; Gortler, Steven et al.
In: Algebraic Statistics, Vol. 14, No. 2, 31.12.2023, p. 287-305.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Bernstein, D, Dewar, S, Gortler, S, Nixon, A, Sitharam, M & Theran, L 2023, 'Computing maximum likelihood thresholds using graph rigidity', Algebraic Statistics, vol. 14, no. 2, pp. 287-305. https://doi.org/10.2140/astat.2023.14.287

APA

Bernstein, D., Dewar, S., Gortler, S., Nixon, A., Sitharam, M., & Theran, L. (2023). Computing maximum likelihood thresholds using graph rigidity. Algebraic Statistics, 14(2), 287-305. https://doi.org/10.2140/astat.2023.14.287

Vancouver

Bernstein D, Dewar S, Gortler S, Nixon A, Sitharam M, Theran L. Computing maximum likelihood thresholds using graph rigidity. Algebraic Statistics. 2023 Dec 31;14(2):287-305. doi: 10.2140/astat.2023.14.287

Author

Bernstein, Daniel ; Dewar, Sean ; Gortler, Steven et al. / Computing maximum likelihood thresholds using graph rigidity. In: Algebraic Statistics. 2023 ; Vol. 14, No. 2. pp. 287-305.

Bibtex

@article{51cd85d1cd344fe7b0848680aeaffb57,
title = "Computing maximum likelihood thresholds using graph rigidity",
abstract = "AbstractThe 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.",
author = "Daniel Bernstein and Sean Dewar and Steven Gortler and Anthony Nixon and Meera Sitharam and Louis Theran",
year = "2023",
month = dec,
day = "31",
doi = "10.2140/astat.2023.14.287",
language = "English",
volume = "14",
pages = "287--305",
journal = "Algebraic Statistics",
issn = "2693-3004",
publisher = "Mathematical Sciences Publishers",
number = "2",

}

RIS

TY - JOUR

T1 - Computing maximum likelihood thresholds using graph rigidity

AU - Bernstein, Daniel

AU - Dewar, Sean

AU - Gortler, Steven

AU - Nixon, Anthony

AU - Sitharam, Meera

AU - Theran, Louis

PY - 2023/12/31

Y1 - 2023/12/31

N2 - AbstractThe 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.

AB - AbstractThe 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.

U2 - 10.2140/astat.2023.14.287

DO - 10.2140/astat.2023.14.287

M3 - Journal article

VL - 14

SP - 287

EP - 305

JO - Algebraic Statistics

JF - Algebraic Statistics

SN - 2693-3004

IS - 2

ER -