Robust Parameter Identifiability Analysis via Column Subset Selection

TL;DR

This paper introduces a numerically reliable method using column subset selection for parameter identifiability analysis, offering advantages over traditional eigenvalue-based methods in accuracy, reliability, and computational efficiency.

Contribution

It proposes a novel CSS-based approach for practical parameter identifiability analysis, improving accuracy and reliability without increasing computational cost.

Findings

CSS methods effectively identify parameter subsets in physical models

Strong rank-revealing QR algorithm provides rigorous accuracy guarantees

CSS approach outperforms eigenvalue methods in numerical experiments

Abstract

We advocate a numerically reliable and accurate approach for practical parameter identifiability analysis: Applying column subset selection (CSS) to the sensitivity matrix, instead of computing an eigenvalue decomposition of the Fischer information matrix. Identifiability analysis via CSS has three advantages: (i) It quantifies reliability of the subsets of parameters selected as identifiable and unidentifiable. (ii) It establishes criteria for comparing the accuracy of different algorithms. (iii) The implementations are numerically more accurate and reliable than eigenvalue methods applied to the Fischer matrix, yet without an increase in computational cost. The effectiveness of the CSS methods is illustrated with extensive numerical experiments on sensitivity matrices from six physical models, as well as on adversarial synthetic matrices. Among the CSS methods, we recommend an implementation based on the strong rank-revealing QR algorithm because of its rigorous accuracy guarantees for both identifiable and non-identifiable parameters.