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Activity Number: 156 - Statistical Aspects in Stochastic and Deterministic Simulation
Type: Topic Contributed
Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract #330084 Presentation
Title: A Latent Variable Approach for Handling Qualitative Factors in Gaussian Process Modeling of Computer Experiments
Author(s): Daniel W Apley* and Yichi Zhang
Companies: Northwestern University and Northwestern University
Keywords: Computer experiments; Gaussian process; Kriging; Spatial statistics; Latent variables
Abstract:

Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and relate them via a multiresponse cross-covariance matrix. We introduce a substantially different approach that maps each qualitative factor to an underlying numerical latent variable (LV), with the mapped value for each level estimated similarly to the covariance lengthscale parameters. This provides a parsimonious GP parameterization that treats qualitative factors the same as numerical variables and views them as effecting the response via similar mechanisms. This has strong physical justification, as the effects of a qualitative factor must always be due to some underlying numerical variables. Even when the underlying variables are many, sufficient dimension reduction arguments imply their effects can be represented by a low-dimensional LV. This is supported by superior predictive performance observed across a variety of examples. Moreover, the mapped LVs provide substantial insight into the nature and effects of the qualitative factors.


Authors who are presenting talks have a * after their name.

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