Gradient-Based Sensitivity Analysis with Kernels

Emulation of computer experiments via surrogate models can be difficult when the number of input parameters determining the simulation grows any greater than a few dozen. In this dissertation, we explore dimension reduction in the context of computer experiments. The active subspace method is a linear dimension reduction technique which uses the gradients of a function to determine important input directions. Unfortunately, we cannot expect to always have access to the gradients of our black-box functions. We thus begin by developing an estimator for the active subspace of a function using kernel methods to indirectly estimate the gradient. We then demonstrate how to deploy the learned input directions to improve the predictive performance of local regression models by ``undoing" the active subspace. Finally, we develop notions of sensitivities which are local to certain parts of the input space, which we then use to develop a Bayesian optimization algorithm which can exploit locally important directions.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2021

Author dc:creator

• Wycoff, Nathan Benjamin

Chair dc:contributor.committeechair

• Gramacy, Robert B.

Committee members dc:contributor.committeemember

• Wild, Stefan M.
• Binois, Mickael
• Leman, Scotland C.
• Higdon, David

• Sensitivity Analysis
• Nonparametric Regression
• Dimension Reduction
• Derivative Free Optimization

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:31835

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/104683