ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Gaussian Processes for Adaptive Design: Learning Non-Stationarity

12 September 2017, 11:40 – 12:10

Abstract

Submitted by
Sébastien Marmin
Authors
Sébastien Marmin (IRSN), David Ginsbourger (Idiap), Jean Baccou (IRSN), Jacques Liandrat (Centrale Marseille)
Abstract
We consider the problem of approximating a function from scarce training samples. We focus on Gaussian process (GP) models, where the objective function is assumed to be a realization of a Gaussian random field. In this Bayesian approach, sequences of new evaluations and final predictions are driven by the assumed prior covariance kernel (through posterior distributions of the objective function) as well as by infill sampling criteria. In many test cases, functions exhibit heterogeneous variations depending on input space regions. It is then common to assume non-stationary prior covariance kernels. Here we define the so-called WaMI class of non-stationary covariance kernels dedicated to functions for which high variations occur along unknown non-canonical directions. Corresponding WaMI GPs generalize both Multiple Index GPs and tensorized warped GPs. We further propose targeted criteria relying on derivatives of the posterior GP. These criteria favour sampling in high variation regions, and we provide formulae for reducing their evaluation. Finally, GP models and criteria are compared on two test cases. On a first mechanical engineering application for nuclear safety, derivative-based criteria are shown to outperform usual variance-based criteria under a stationary model. Yet, prediction errors are even lower when combining variance-based criteria with WaMI GP. Treed Gaussian Processes are also compared on this and a second application from NASA, on which it first outperforms WaMI on small data set but is overcome by WaMI GP in sequential settings.

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