Regression Approximations to Estimate Sensitivities
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.
- Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning. Data Mining, Inference, and Prediction, 2nd edn. Springer Science & Business Media, New YorkGoogle Scholar