On the existence of identifiable reparametrizations for linear compartment models

TL;DR

This paper investigates conditions under which unidentifiable linear compartment models can be reparametrized to become identifiable, using algebraic geometry and graph theory to develop new criteria and constructions.

Contribution

It introduces a new rank-based criterion for the existence of identifiable reparametrizations and provides methods to modify models to achieve identifiability.

Findings

Derived new graph-based criterion for reparametrization existence

Constructed classes of graphs with identifiable reparametrizations

Proposed procedures to modify models for identifiability

Abstract

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.