title: Numerical algebraic geometry for model selection and its application to the life sciences.
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.
authors.affiliation: Department of Mathematics, San José State University, San José, CA 95112, USA.
authors.forename: Elizabeth
authors.initials: E
authors.lastname: Gross
authors.affiliation: Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA.
authors.forename: Brent
authors.initials: B
authors.lastname: Davis
authors.affiliation: Department of Mathematics, Stanford University, Stanford, CA 94305, USA.
authors.forename: Kenneth L
authors.initials: KL
authors.lastname: Ho
authors.affiliation: Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA.
authors.forename: Daniel J
authors.initials: DJ
authors.lastname: Bates
authors.affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK harrington@maths.ox.ac.uk.
authors.forename: Heather A
authors.identifier: 0000-0002-1705-7869
authors.initials: HA
authors.lastname: Harrington
mesh_terms: D008954:Models, Biological
keywords: chemical reaction networks; maximum-likelihood; model validation; parameter estimation; polynomial optimization