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

Handle URI:
http://hdl.handle.net/10754/623572
Title:
Numerical algebraic geometry for model selection and its application to the life sciences
Authors:
Gross, Elizabeth; Davis, Brent; Ho, Kenneth L.; Bates, Daniel J.; Harrington, Heather A. ( 0000-0002-1705-7869 )
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.
Citation:
Gross E, Davis B, Ho KL, Bates DJ, Harrington HA (2016) Numerical algebraic geometry for model selection and its application to the life sciences. Journal of The Royal Society Interface 13: 20160256. Available: http://dx.doi.org/10.1098/rsif.2016.0256.
Publisher:
The Royal Society
Journal:
Journal of The Royal Society Interface
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
12-Oct-2016
DOI:
10.1098/rsif.2016.0256
Type:
Article
ISSN:
1742-5689; 1742-5662
Sponsors:
E.G., K.L.H., D.J.B. and H.A.H. acknowledge funding from the American Institute of Mathematics (AIM). E.G. was supported by the US National Science Foundation grant DMS-1304167. B.D. was partially supported by NSF DMS-1115668. K.L.H. acknowledges support from NSF DMS-1203554. D.J.B. gratefully acknowledges partial support from NSF DMS-1115668, NSF ACI-1440467, and the Mathematical Biosciences Institute (MBI). H.A.H. gratefully acknowledges funding from AMS Simons Travel Grant, EPSRC Fellowship EP/K041096/1, King Abdullah University of Science and Technology (KAUST) KUK-C1-013-04 and MPH Stumpf Leverhulme Trust Grant.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorGross, Elizabethen
dc.contributor.authorDavis, Brenten
dc.contributor.authorHo, Kenneth L.en
dc.contributor.authorBates, Daniel J.en
dc.contributor.authorHarrington, Heather A.en
dc.date.accessioned2017-05-15T10:35:09Z-
dc.date.available2017-05-15T10:35:09Z-
dc.date.issued2016-10-12en
dc.identifier.citationGross E, Davis B, Ho KL, Bates DJ, Harrington HA (2016) Numerical algebraic geometry for model selection and its application to the life sciences. Journal of The Royal Society Interface 13: 20160256. Available: http://dx.doi.org/10.1098/rsif.2016.0256.en
dc.identifier.issn1742-5689en
dc.identifier.issn1742-5662en
dc.identifier.doi10.1098/rsif.2016.0256en
dc.identifier.urihttp://hdl.handle.net/10754/623572-
dc.description.abstractResearchers 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.en
dc.description.sponsorshipE.G., K.L.H., D.J.B. and H.A.H. acknowledge funding from the American Institute of Mathematics (AIM). E.G. was supported by the US National Science Foundation grant DMS-1304167. B.D. was partially supported by NSF DMS-1115668. K.L.H. acknowledges support from NSF DMS-1203554. D.J.B. gratefully acknowledges partial support from NSF DMS-1115668, NSF ACI-1440467, and the Mathematical Biosciences Institute (MBI). H.A.H. gratefully acknowledges funding from AMS Simons Travel Grant, EPSRC Fellowship EP/K041096/1, King Abdullah University of Science and Technology (KAUST) KUK-C1-013-04 and MPH Stumpf Leverhulme Trust Grant.en
dc.publisherThe Royal Societyen
dc.subjectChemical reaction networksen
dc.subjectMaximum-likelihooden
dc.subjectModel validationen
dc.subjectParameter estimationen
dc.subjectPolynomial optimizationen
dc.titleNumerical algebraic geometry for model selection and its application to the life sciencesen
dc.typeArticleen
dc.identifier.journalJournal of The Royal Society Interfaceen
dc.contributor.institutionDepartment of Mathematics, San Jose´ State University, San Jose´, CA 95112, USAen
dc.contributor.institutionDepartment of Mathematics, Colorado State University, Fort Collins, CO 80523, USAen
dc.contributor.institutionDepartment of Mathematics, Stanford University, Stanford, CA 94305, USAen
dc.contributor.institutionMathematical Institute, University of Oxford, Oxford OX2 6GG, UKen
kaust.grant.numberKUK-C1-013-04en
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