Adaptive Design of Experiments for Conservative Estimation of Excursion Sets

Dario Azzimonti (1, 2) , David Ginsbourger (2, 1) , Clément Chevalier (3) , Julien Bect (4, 5) , Yann Richet (6, 5)

1 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
2 Idiap - Idiap Research Institute
3 UNINE - Institut de Statistique [Neuchâtel]
4 L2S - Laboratoire des signaux et systèmes
5 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
6 IRSN - Institut de Radioprotection et de Sûreté Nucléaire

We consider a Gaussian process model trained on few evaluations of an expensive-to-evaluate deterministic function and we study the problem of estimating a fixed excursion set of this function. We review the concept of conservative estimates, recently introduced in this framework, and, in particular, we focus on estimates based on Vorob'ev quantiles. We present a method that sequentially selects new evaluations of the function in order to reduce the uncertainty on such estimates. The sequential strategies are first benchmarked on artificial test cases generated from Gaussian process realizations in two and five dimensions, and then applied to two reliability engineering test cases.

Mots clés: Excursion sets; Adaptive design of experiments; Gaussian process models; Conservative estimates; Batch sequential strategies

Domaines: Méthodologie [stat.ME]; Machine Learning [stat.ML]; Statistiques [math.ST]

Dario Azzimonti, David Ginsbourger, Clément Chevalier, Julien Bect, Yann Richet. Adaptive Design of Experiments for Conservative Estimation of Excursion Sets. 2017. ⟨hal-01379642v2⟩