Inverse regression for ridge recovery: a data-driven approach for parameter reduction in computer experiments

Andrew Glaws, Paul G. Constantine, R. D Cook

Research output: Contribution to journalArticle

Abstract

Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction (SDR) use data to reduce the predictor dimension of a regression problem. A computational scientist hoping to use SDR for parameter reduction encounters a problem: a computer prediction is best represented by a deterministic function of the inputs, so data comprised of computer simulation queries fail to satisfy the SDR assumptions. To address this problem, we interpret SDR methods sliced inverse regression (SIR) and sliced average variance estimation (SAVE) as estimating the directions of a ridge function, which is a composition of a low-dimensional linear transformation with a nonlinear function. Within this interpretation, SIR and SAVE estimate matrices of integrals whose column spaces are contained in the ridge directions’ span; we analyze and numerically verify convergence of these column spaces as the number of computer model queries increases. Moreover, we show example functions that are not ridge functions but whose inverse conditional moment matrices are low-rank. Consequently, the computational scientist should beware when using SIR and SAVE for parameter reduction, since SIR and SAVE may mistakenly suggest that truly important directions are unimportant.

Original languageEnglish (US)
JournalStatistics and Computing
DOIs
StatePublished - Jan 1 2019

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Sliced Average Variance Estimation
Inverse Regression
Sufficient Dimension Reduction
Sliced Inverse Regression
Computer Experiments
Ridge
Data-driven
Recovery
Column space
Ridge Functions
Regression
Experiments
Query
Moment Matrix
Conditional Moments
Computational Science
Computer Model
Linear transformation
Reduction Method
Nonlinear Function

Keywords

  • Ridge functions
  • Ridge recovery
  • Sufficient dimension reduction

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Inverse regression for ridge recovery : a data-driven approach for parameter reduction in computer experiments. / Glaws, Andrew; Constantine, Paul G.; Cook, R. D.

In: Statistics and Computing, 01.01.2019.

Research output: Contribution to journalArticle

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