Identifiability in Continuous Lyapunov Models
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Identifiability in Continuous Lyapunov Models. / Dettling, Philipp; Homs, Roser; Amendola, Carlos; Drton, Mathias; Hansen, Niels Richard.
I: SIAM Journal on Matrix Analysis and Applications, Bind 44, Nr. 4, 2023, s. 1799-1821.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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