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Regression Approximations to Estimate Sensitivities

  • Ryan G. McClarren
Chapter

Abstract

Chapter 5 explores the idea of using regression problems to estimate sensitivities. Section 5.1 explains how one might approximate the gradient of the QoI at a nominal point using a least-squares (regression) formulation. This naive approach requires more QoI evaluations than one-sided finite differences as described in the previous chapter. Section 5.2 introduces a regularization term into the least-squares minimization problem, allowing for useful solutions also for the case where fewer QoI evaluations than parameters are available; sparsity-promoting regularization (1-norm, LASSO) and a combination of 1-norm and 2-norm (elastic net) are considered. Section 5.3 adds cross-validation techniques for selecting the regularization parameters.

References

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ryan G. McClarren
    • 1
  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA

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