Numerical algebraic geometry for model selection and its application to the life sciences

Elizabeth Gross, Brent Davis, Kenneth L. Ho, Daniel J. Bates, Heather A. Harrington

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology.
Original languageEnglish (US)
Pages (from-to)20160256
JournalJournal of the Royal Society Interface
Volume13
Issue number123
DOIs
StatePublished - Oct 12 2016
Externally publishedYes

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