Computational Methods for Estimating Global Sensitivity Indices and Shapley Values

Global sensitivity analysis studies how uncertainty in a model's output can be attributed to uncertainties in the model's inputs. This analysis has applications in various fields such as natural sciences, engineering, social sciences, and mathematical sciences. Several global sensitivity analysis methods have been introduced in literature, such as Sobol' sensitivity indices, activity scores, derivative-based global sensitivity measures (DGSM), and Shapley values. The dissertation introduces two new control variate Monte Carlo estimators based on the truncated sparse polynomial chaos expansion of the function in hand. The control variate estimators are used to estimate the lower and upper Sobol' indices in some applications, and are numerically compared with some of the best Monte Carlo estimators in the literature. The results suggest that the control variate estimators are either the best or among the best in terms of efficiency in computationally expensive problems where a low-order polynomial chaos expansion is not an accurate approximation of the model but highly correlated with it. We also introduce two new approaches to Shapley values, that are based on the first-order partial derivatives and the finite-differences of the underlying function. The derivative based Shapley value has linear computational complexity in the number of features, as opposed to the exponential complexity of other Shapley value approaches. The finite-difference based method is especially useful when there are high-order interactions or in the presence of noise. The methods are used for global sensitivity analysis and machine learning explainability, and numerical comparisons with activity scores, global activity scores, SHAP, and KernelSHAP are provided.

Grantor dc:publisher

Florida State University

Year dc:date

2023

Contributors dc:contributor

• Duan, Hui (author)
• Ökten, Giray (professor directing dissertation)
• Liu, Xiuwen, 1966- (university representative)
• Zhu, Lingjiong (committee member)
• Bao, Feng (committee member)
• Florida State University (degree granting institution)
• College of Arts and Sciences (degree granting college)
• Department of Mathematics (degree granting department)

• Mathematics

Language dc:language

English

Identifier

fsu:927881
iid: Duan_fsu_0071E_18115

OAI identifier oai:identifier

oai:diginole.lib.fsu.edu:fsu_927881