Multiresolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

Chih Li Sung*, Wenjia Wang, Matthew Plumlee, Benjamin Haaland

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multiresolution functional ANOVA (MRFA) model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input nonlinear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed MRFA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, in terms of both sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)908-919
Number of pages12
JournalJournal of the American Statistical Association
Volume115
Issue number530
DOIs
StatePublished - Apr 2 2020

Keywords

  • Computer experiments
  • Large-scale
  • Many-input
  • Nonlinear regression
  • Overlapping group lasso

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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