The maximum likelihood degree of toric varieties

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

The maximum likelihood degree of toric varieties. / Améndola, Carlos; Bliss, Nathan; Burke, Isaac; Gibbons, Courtney R.; Helmer, Martin; Hoşten, Serkan; Nash, Evan D.; Rodriguez, Jose Israel; Smolkin, Daniel.

In: Journal of Symbolic Computation, Vol. 92, 2018, p. 222-242.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Améndola, C, Bliss, N, Burke, I, Gibbons, CR, Helmer, M, Hoşten, S, Nash, ED, Rodriguez, JI & Smolkin, D 2018, 'The maximum likelihood degree of toric varieties', Journal of Symbolic Computation, vol. 92, pp. 222-242. https://doi.org/10.1016/j.jsc.2018.04.016

APA

Améndola, C., Bliss, N., Burke, I., Gibbons, C. R., Helmer, M., Hoşten, S., Nash, E. D., Rodriguez, J. I., & Smolkin, D. (2018). The maximum likelihood degree of toric varieties. Journal of Symbolic Computation, 92, 222-242. https://doi.org/10.1016/j.jsc.2018.04.016

Vancouver

Améndola C, Bliss N, Burke I, Gibbons CR, Helmer M, Hoşten S et al. The maximum likelihood degree of toric varieties. Journal of Symbolic Computation. 2018;92:222-242. https://doi.org/10.1016/j.jsc.2018.04.016

Author

Améndola, Carlos ; Bliss, Nathan ; Burke, Isaac ; Gibbons, Courtney R. ; Helmer, Martin ; Hoşten, Serkan ; Nash, Evan D. ; Rodriguez, Jose Israel ; Smolkin, Daniel. / The maximum likelihood degree of toric varieties. In: Journal of Symbolic Computation. 2018 ; Vol. 92. pp. 222-242.

Bibtex

@article{bef44311e7a14f1a85376e92eb4e71fb,
title = "The maximum likelihood degree of toric varieties",
abstract = "We study the maximum likelihood (ML) degree of toric varieties, known as discrete exponential models in statistics. By introducing scaling coefficients to the monomial parameterization of the toric variety, one can change the ML degree. We show that the ML degree is equal to the degree of the toric variety for generic scalings, while it drops if and only if the scaling vector is in the locus of the principal A-determinant. We also illustrate how to compute the ML estimate of a toric variety numerically via homotopy continuation from a scaled toric variety with low ML degree. Throughout, we include examples motivated by algebraic geometry and statistics. We compute the ML degree of rational normal scrolls and a large class of Veronese-type varieties. In addition, we investigate the ML degree of scaled Segre varieties, hierarchical log-linear models, and graphical models.",
keywords = "A-discriminant, Maximum likelihood degree, Toric variety",
author = "Carlos Am{\'e}ndola and Nathan Bliss and Isaac Burke and Gibbons, {Courtney R.} and Martin Helmer and Serkan Ho{\c s}ten and Nash, {Evan D.} and Rodriguez, {Jose Israel} and Daniel Smolkin",
year = "2018",
doi = "10.1016/j.jsc.2018.04.016",
language = "English",
volume = "92",
pages = "222--242",
journal = "Journal of Symbolic Computation",
issn = "0747-7171",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - The maximum likelihood degree of toric varieties

AU - Améndola, Carlos

AU - Bliss, Nathan

AU - Burke, Isaac

AU - Gibbons, Courtney R.

AU - Helmer, Martin

AU - Hoşten, Serkan

AU - Nash, Evan D.

AU - Rodriguez, Jose Israel

AU - Smolkin, Daniel

PY - 2018

Y1 - 2018

N2 - We study the maximum likelihood (ML) degree of toric varieties, known as discrete exponential models in statistics. By introducing scaling coefficients to the monomial parameterization of the toric variety, one can change the ML degree. We show that the ML degree is equal to the degree of the toric variety for generic scalings, while it drops if and only if the scaling vector is in the locus of the principal A-determinant. We also illustrate how to compute the ML estimate of a toric variety numerically via homotopy continuation from a scaled toric variety with low ML degree. Throughout, we include examples motivated by algebraic geometry and statistics. We compute the ML degree of rational normal scrolls and a large class of Veronese-type varieties. In addition, we investigate the ML degree of scaled Segre varieties, hierarchical log-linear models, and graphical models.

AB - We study the maximum likelihood (ML) degree of toric varieties, known as discrete exponential models in statistics. By introducing scaling coefficients to the monomial parameterization of the toric variety, one can change the ML degree. We show that the ML degree is equal to the degree of the toric variety for generic scalings, while it drops if and only if the scaling vector is in the locus of the principal A-determinant. We also illustrate how to compute the ML estimate of a toric variety numerically via homotopy continuation from a scaled toric variety with low ML degree. Throughout, we include examples motivated by algebraic geometry and statistics. We compute the ML degree of rational normal scrolls and a large class of Veronese-type varieties. In addition, we investigate the ML degree of scaled Segre varieties, hierarchical log-linear models, and graphical models.

KW - A-discriminant

KW - Maximum likelihood degree

KW - Toric variety

UR - http://www.scopus.com/inward/record.url?scp=85045325960&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2018.04.016

DO - 10.1016/j.jsc.2018.04.016

M3 - Journal article

AN - SCOPUS:85045325960

VL - 92

SP - 222

EP - 242

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

ER -

ID: 199804620