Session: Methods for Uncertainty Quantification, Sensitivity Analysis, and Prediction

Paper Number: 157688

157688 - Variable Selection in Optimization Using Quantile-Based Sensitivity Indices 

Abstract: 

Fixing unimportant variables to reduce the number of dimensions in optimization problems has shown to dramatically reduce convergence time with minimal loss in accuracy. This method is crucial for high-dimensional problems and/or computationally expensive objective functions. In variable selection, important variables are identified in an initial screening step and optimization is carried out on the important variables. The unimportant variables are fixed at the optimum values that were estimated during the initial screening step. Sensitivity indices can be used to identify important variables. Many widely used dimension reduction methods and sensitivity indices, such as Sobol' indices, measure variable impact on the variance of the output. These variance-based sensitivity indices measure variable impact on the expectation of the output, which is not well-suited for optimization since the minimum or maximum of an objective function is desired. The use of sensitivity indices in optimization is recent. Therefore, this work proposes the use of quantile-based sensitivity indices for variable selection in optimization. These indices measure the contribution of variables to the lower/upper quantiles or lower/upper tails of the output distribution. This work presents the methodology and application of Quantile-based Shapley effects (QSHAP), Quantile-Oriented Sensitivity Analysis (QOSA) indices, and Quantile-based Global Sensitivity Measure (QGSM) indices in optimization and compares them to the already proposed Hilbert-Schmidt Independence Criterion with Indicator Thresholding (HSIC-IT) indices. QSHAP indices are computed from the Shapley effects of the data within the tail of the output distribution and measures the contribution of variables to the variance within the tail of the output. QOSA indices are based on contrast functions and are a special case of goal-oriented sensitivity indices, where the quantile of the output distribution is quantity of interest.  QGSM indices measure the expectation of the squared or absolute distance between the output distribution and the conditional distribution given the variable of interest. All three of these quantile-based sensitivity indices have a link to Sobol' indices. Other researchers have proposed HSIC-IT indices to measure the dependence between the distribution of the input variables and the output distribution.  In HSIC-IT, an indicator function is applied to the output so that the left or right tail consists of ones. The ability of these indices to correctly identify important variables for optimization was tested on several benchmark examples and compared to the existing HSIC-IT indices. In practice, these indices need to be computed from a limited number of data points, possibly with the use of surrogate models. The computational performance and accuracy of these indices were assessed on several high-dimensional practical applications. It was shown that these quantile-based sensitivity indices can be effective for variable selection in optimization; however, the QSHAP indices performed the best.

Presenting Author: Matthew Balcer Los Alamos National Laboratory

Presenting Author Biography: Postdoctoral researcher at Los Alamos National Laboratory in the Verification and Analysis group.

Authors:

Matthew Balcer Los Alamos National Laboratory
Derek Armstrong Los Alamos National Laboratory