On the existence of identifiable reparametrizations for linear compartment models

Baaijens, Jasmijn A.; Draisma, Jan (2016). On the existence of identifiable reparametrizations for linear compartment models. SIAM journal on applied mathematics, 76(4), pp. 1577-1605. Society for Industrial and Applied Mathematics 10.1137/15M1038013

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The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case, one can search for an identifiable reparametrization of the model: a map which reduces the number of parameters, such that the reduced model is identifiable. We study a specific class of models which are known to be unidentifiable. Using algebraic geometry and graph theory, we translate a criterion given by Meshkat and Sullivant for the existence of an identifiable scaling reparametrization to a new criterion based on the rank of a weighted adjacency matrix of a certain bipartite graph. This allows us to derive several new constructions to obtain graphs with an identifiable scaling reparametrization. Using these constructions, a large subclass of such graphs is obtained. Finally, we present a procedure of subdividing or deleting edges to ensure that a model has an identifiable scaling reparametrization.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Draisma, Jan

Subjects:

500 Science > 510 Mathematics

ISSN:

0036-1399

Publisher:

Society for Industrial and Applied Mathematics

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

07 Aug 2017 16:54

Last Modified:

07 Aug 2017 16:54

Publisher DOI:

10.1137/15M1038013

ArXiv ID:

1509.02551v2

BORIS DOI:

10.7892/boris.99757

URI:

https://boris.unibe.ch/id/eprint/99757

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