Identifiability of Linear Compartmental Models: The Impact of Removing Leaks and Edges

TL;DR

This paper investigates how the identifiability of linear compartmental models is affected by removing leaks or edges, providing proofs for specific cases and relating the problem to the singular-locus equation.

Contribution

It proves a special case of Gross et al.'s conjecture on leak removal and establishes a link between leak terms and the singular-locus equation, advancing understanding of model identifiability.

Findings

Removing a leak from an identifiable model can preserve identifiability in certain cases.

Removing specific edges that divide the singular-locus equation can lead to unidentifiability.

The paper proves a case of the conjecture that edge removal affects identifiability.

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.