Fast Prediction of Deterministic Functions Using Sparse Grid Experimental Designs

Matthew Plumlee*

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the computational burden it requires. This problem is often seen in cases where the input of the expensive function is high dimensional. While many previous works have focused on developing an approximative predictor to resolve these issues, this article investigates a different solution mechanism. We demonstrate that when a general set of designs is employed, the resulting predictor is quick to compute and has reasonable accuracy. The fast computation of the predictor is made possible through an algorithm proposed by this work. This article also demonstrates methods to quickly evaluate the likelihood of the observations and describes some fast maximum likelihood estimates for unknown parameters of the random field. The computational savings can be several orders of magnitude when the input is located in a high-dimensional space. Beyond the fast computation of the predictor, existing research has demonstrated that a subset of these designs generate predictors that are asymptotically efficient. This work details some empirical comparisons to the more common space-filling designs that verify the designs are competitive in terms of resulting prediction accuracy.

Original languageEnglish (US)
Pages (from-to)1581-1591
Number of pages11
JournalJournal of the American Statistical Association
Volume109
Issue number508
DOIs
StatePublished - Oct 2 2014

Keywords

  • Computer experiment
  • Gaussian process
  • High-dimensional input
  • Large-scale experiment
  • Simulation experiment

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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