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Database for identifiability properties of linear compartmental models

Natali Gogishvili

TL;DR

The paper tackles the problem of structural identifiability in linear compartmental models, focusing on whether parameters can be uniquely, finitely, or infinitely inferred from noise-free time-series data. The authors assemble a comprehensive database of linear compartment models up to four compartments, reduced by graph isomorphism to improve efficiency, and provide tooling to query identifiability results. They use the database to test conjectures, notably disproving Conjecture 4.5 on deleting leaks by identifying minimal counterexamples and validating with independent identifiability tools. The work offers identifiability statistics and a practical resource that supports theorem verification and insight into how model structure affects identifiability.

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.

Database for identifiability properties of linear compartmental models

TL;DR

The paper tackles the problem of structural identifiability in linear compartmental models, focusing on whether parameters can be uniquely, finitely, or infinitely inferred from noise-free time-series data. The authors assemble a comprehensive database of linear compartment models up to four compartments, reduced by graph isomorphism to improve efficiency, and provide tooling to query identifiability results. They use the database to test conjectures, notably disproving Conjecture 4.5 on deleting leaks by identifying minimal counterexamples and validating with independent identifiability tools. The work offers identifiability statistics and a practical resource that supports theorem verification and insight into how model structure affects identifiability.

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.

Paper Structure

This paper contains 9 sections, 1 equation, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Linear Compartment Models
  4. Parameter identifiability
  5. The database
  6. Application: identifiability statistics
  7. Application: counterexample to the conjecture
  8. Conclusions
  9. Acknowledgements

Figures (5)

  • Figure 1: Identifiability statistics over number of nodes, leaks, and inputs.
  • Figure 1: Illustration of one of the models before and after removing the leak.
  • Figure 1: Illustration of one of the models before and after removing the leak.
  • Figure 2: Example of the model which is locally identifiable
  • Figure 2: Heat-maps of results. Number of inputs over number of leaks.