Identifiability of Linear Compartmental Models: The Impact of Removing Leaks and Edges
Abstract
A mathematical model is identifiable if its parameters can be recovered from data. Here, we focus on a particular class of model, linear compartmental models, which are used to represent the transfer of substances in a system. We analyze what happens to identifiability when operations are performed on a model, specifically, adding or deleting a leak or an edge. We first consider the conjecture of Gross et al. that states that removing a leak from an identifiable model yields a model that is again identifiable. We prove a special case of this conjecture, and also show that the conjecture is equivalent to asserting that leak terms do not divide the so-called singular-locus equation. As for edge terms that do divide this equation, we conjecture that removing any one of these edges makes the model become unidentifiable,and then prove a case of this somewhat surprising conjecture.
Keywords
Cite
@article{arxiv.2102.04417,
title = {Identifiability of Linear Compartmental Models: The Impact of Removing Leaks and Edges},
author = {Patrick Chan and Katherine Johnston and Anne Shiu and Aleksandra Sobieska and Clare Spinner},
journal= {arXiv preprint arXiv:2102.04417},
year = {2021}
}
Comments
15 pages, 6 figures. Updated paper in light of conjecture now solved