Database for identifiability properties of linear compartmental models

TL;DR

This paper introduces a database of linear compartment models with their identifiability properties, aiding researchers in quickly assessing whether model parameters can be uniquely inferred from data.

Contribution

The authors created a memory-efficient database of linear compartment models with known identifiability results, facilitating theorem checking and hypothesis testing.

Findings

Counterexample to a conjecture about leak deletion in models

Database enables quick identifiability checks

Statistics on parameter identifiability in models

Abstract

Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable. Global identifiability of the parameter indicates that there exists only one possible solution to the inference problem, local identifiability suggests that there could be several (but finitely many) possibilities, while non-identifiability implies that there are infinitely many possibilities for the value. Having this information is useful since, one would, for example, only perform inferences for the parameters which are identifiable. Given the current significance and widespread research conducted in this area, we decided to create a database of linear compartment models and their identifiability results. This facilitates the process of checking theorems and conjectures and drawing conclusions on identifiability. By only storing models up to symmetries and isomorphisms, we optimize memory efficiency and reduce query time. We conclude by applying our database to real problems. We tested a conjecture about deleting one leak of the model states in the paper 'Linear compartmental models: Input-output equations and operations that preserve identifiability' by E. Gross et al., and managed to produce a counterexample. We also compute some interesting statistics related to the identifiability of linear compartment model parameters.