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

Elizabeth Gross1, Brent Davis2, Kenneth L Ho3

  • 1Department of Mathematics, San José State University, San José, CA 95112, USA.

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|October 14, 2016
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Summary
This summary is machine-generated.

This study presents a novel framework for analyzing polynomial models, tackling challenges in parameter estimation and model selection using numerical algebraic geometry. The method efficiently identifies global optima from complex optimization problems, even with limited data.

Keywords:
chemical reaction networksmaximum-likelihoodmodel validationparameter estimationpolynomial optimization

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Area of Science:

  • Mathematical modeling
  • Computational algebraic geometry

Background:

  • Parameter estimation, model validation, and selection are critical optimization problems in mathematical modeling.
  • These problems are often complex due to nonlinearity, non-convexity, multiple local optima, and limited data.

Purpose of the Study:

  • To introduce a computational framework for analyzing polynomial models.
  • To address the challenges of parameter estimation, model validation, and selection in optimization problems.

Main Methods:

  • Utilizing numerical algebraic geometry, specifically probability-one polynomial homotopy continuation methods.
  • Computing all critical points of the objective function and filtering to identify global optima.
  • Exploiting geometrical structures relating models and data.

Main Results:

  • A robust framework for optimization problems associated with polynomial models.
  • Successful application demonstrated on examples from cell signaling, synthetic biology, and epidemiology.
  • Efficient computation of global optima even with partial data.

Conclusions:

  • The proposed numerical algebraic geometry framework offers a powerful approach to solving complex optimization problems in mathematical modeling.
  • This method enhances the analysis of polynomial models, particularly in data-limited scenarios.
  • The utility is validated across diverse scientific domains.