Identifiability in Continuous Lyapunov Models

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

Standard

Identifiability in Continuous Lyapunov Models. / Dettling, Philipp; Homs, Roser; Amendola, Carlos; Drton, Mathias; Hansen, Niels Richard.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 4, 2023, p. 1799-1821.

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

Harvard

Dettling, P, Homs, R, Amendola, C, Drton, M & Hansen, NR 2023, 'Identifiability in Continuous Lyapunov Models', SIAM Journal on Matrix Analysis and Applications, vol. 44, no. 4, pp. 1799-1821. https://doi.org/10.1137/22M1520311

APA

Dettling, P., Homs, R., Amendola, C., Drton, M., & Hansen, N. R. (2023). Identifiability in Continuous Lyapunov Models. SIAM Journal on Matrix Analysis and Applications, 44(4), 1799-1821. https://doi.org/10.1137/22M1520311

Vancouver

Dettling P, Homs R, Amendola C, Drton M, Hansen NR. Identifiability in Continuous Lyapunov Models. SIAM Journal on Matrix Analysis and Applications. 2023;44(4):1799-1821. https://doi.org/10.1137/22M1520311

Author

Dettling, Philipp ; Homs, Roser ; Amendola, Carlos ; Drton, Mathias ; Hansen, Niels Richard. / Identifiability in Continuous Lyapunov Models. In: SIAM Journal on Matrix Analysis and Applications. 2023 ; Vol. 44, No. 4. pp. 1799-1821.

Bibtex

@article{0b2de65a2c0942fa836378a3908ad0c2,
title = "Identifiability in Continuous Lyapunov Models",
abstract = "The recently introduced graphical continuous Lyapunov models provide a new approach to statistical modeling of correlated multivariate data. The models view each observation as a one-time cross-sectional snapshot of a multivariate dynamic process in equilibrium. The covariance matrix for the data is obtained by solving a continuous Lyapunov equation that is parametrized by the drift matrix of the dynamic process. In this context, different statistical models postulate different sparsity patterns in the drift matrix, and it becomes a crucial problem to clarify whether a given sparsity assumption allows one to uniquely recover the drift matrix parameters from the covariance matrix of the data. We study this identifiability problem by representing sparsity patterns by directed graphs. Our main result proves that the drift matrix is globally identifiable if and only if the graph for the sparsity pattern is simple (i.e., does not contain directed 2-cycles). Moreover, we present a necessary condition for generic identifiability and provide a computational classification of small graphs with up to 5 nodes.",
keywords = "graphical modeling, identifiability, Lyapunov equation",
author = "Philipp Dettling and Roser Homs and Carlos Amendola and Mathias Drton and Hansen, {Niels Richard}",
note = "Publisher Copyright: 1799 {\textcopyright} by SIAM. Unauthorized reproduction of this article is prohibited.",
year = "2023",
doi = "10.1137/22M1520311",
language = "English",
volume = "44",
pages = "1799--1821",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",

}

RIS

TY - JOUR

T1 - Identifiability in Continuous Lyapunov Models

AU - Dettling, Philipp

AU - Homs, Roser

AU - Amendola, Carlos

AU - Drton, Mathias

AU - Hansen, Niels Richard

N1 - Publisher Copyright: 1799 © by SIAM. Unauthorized reproduction of this article is prohibited.

PY - 2023

Y1 - 2023

N2 - The recently introduced graphical continuous Lyapunov models provide a new approach to statistical modeling of correlated multivariate data. The models view each observation as a one-time cross-sectional snapshot of a multivariate dynamic process in equilibrium. The covariance matrix for the data is obtained by solving a continuous Lyapunov equation that is parametrized by the drift matrix of the dynamic process. In this context, different statistical models postulate different sparsity patterns in the drift matrix, and it becomes a crucial problem to clarify whether a given sparsity assumption allows one to uniquely recover the drift matrix parameters from the covariance matrix of the data. We study this identifiability problem by representing sparsity patterns by directed graphs. Our main result proves that the drift matrix is globally identifiable if and only if the graph for the sparsity pattern is simple (i.e., does not contain directed 2-cycles). Moreover, we present a necessary condition for generic identifiability and provide a computational classification of small graphs with up to 5 nodes.

AB - The recently introduced graphical continuous Lyapunov models provide a new approach to statistical modeling of correlated multivariate data. The models view each observation as a one-time cross-sectional snapshot of a multivariate dynamic process in equilibrium. The covariance matrix for the data is obtained by solving a continuous Lyapunov equation that is parametrized by the drift matrix of the dynamic process. In this context, different statistical models postulate different sparsity patterns in the drift matrix, and it becomes a crucial problem to clarify whether a given sparsity assumption allows one to uniquely recover the drift matrix parameters from the covariance matrix of the data. We study this identifiability problem by representing sparsity patterns by directed graphs. Our main result proves that the drift matrix is globally identifiable if and only if the graph for the sparsity pattern is simple (i.e., does not contain directed 2-cycles). Moreover, we present a necessary condition for generic identifiability and provide a computational classification of small graphs with up to 5 nodes.

KW - graphical modeling

KW - identifiability

KW - Lyapunov equation

U2 - 10.1137/22M1520311

DO - 10.1137/22M1520311

M3 - Journal article

AN - SCOPUS:85179759944

VL - 44

SP - 1799

EP - 1821

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 4

ER -

ID: 377443487