Adaptive Design of Experiments for Conservative Estimation of Excursion Sets

Autor: Yann Richet, Clément Chevalier, Julien Bect, David Ginsbourger, Dario Azzimonti
Přispěvatelé: Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), Università della Svizzera italiana = University of Italian Switzerland (USI)-Scuola universitaria professionale della Svizzera italiana [Manno] (SUPSI), IDIAP Research Institute, Institute of Mathematical Statistics and Actuarial Science [Bern] (IMSV), University of Bern, Université de Neuchâtel (UNINE), Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSE-ENV/SCAN, Idiap Research Institute (Idiap), Institut de Statistique [Neuchâtel] (UNINE), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2019
Předmět:
Statistics and Probability
FOS: Computer and information sciences
Batch sequential strategies
Mathematical optimization
Gaussian process model
Computer science
0211 other engineering and technologies
Machine Learning (stat.ML)
Mathematics - Statistics Theory
02 engineering and technology
Statistics Theory (math.ST)
01 natural sciences
Set (abstract data type)
Methodology (stat.ME)
010104 statistics & probability
symbols.namesake
510 Mathematics
[STAT.ML]Statistics [stat]/Machine Learning [stat.ML]
Statistics - Machine Learning
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
False positive paradox
FOS: Mathematics
0101 mathematics
Adaptive design of experiments
Gaussian process
Uncertainty reduction theory
Statistics - Methodology
ComputingMilieux_MISCELLANEOUS
021103 operations research
Applied Mathematics
Design of experiments
Excursion
Function (mathematics)
Conservative estimates
Computer experiment
Excursion sets
Modeling and Simulation
symbols
[STAT.ME]Statistics [stat]/Methodology [stat.ME]
Stepwise Uncertainty Reduction
360 Social problems & social services
Zdroj: INI workshop on "Key UQ methodologies and motivating applications" (UNQW01)
INI workshop on "Key UQ methodologies and motivating applications" (UNQW01), Jan 2018, Cambridge, United Kingdom
Technometrics
Technometrics, Taylor & Francis, 2021, 63 (1), pp.13-26. ⟨10.1080/00401706.2019.1693427⟩
ISSN: 0040-1706
1537-2723
DOI: 10.6084/m9.figshare.10358789
Popis: We consider the problem of estimating the set of all inputs that leads a system to some particular behavior. The system is modeled by an expensive-to-evaluate function, such as a computer experiment, and we are interested in its excursion set, that is, the set of points where the function takes values above or below some prescribed threshold. The objective function is emulated with a Gaussian process (GP) model based on an initial design of experiments enriched with evaluation results at (batch-) sequentially determined input points. The GP model provides conservative estimates for the excursion set, which control false positives while minimizing false negatives. We introduce adaptive strategies that sequentially select new evaluations of the function by reducing the uncertainty on conservative estimates. Following the stepwise uncertainty reduction approach we obtain new evaluations by minimizing adapted criteria. Tractable formulas for the conservative criteria are derived, which allow more convenient optimization. The method is benchmarked on random functions generated under the model assumptions in different scenarios of noise and batch size. We then apply it to a reliability engineering test case. Overall, the proposed strategy of minimizing false negatives in conservative estimation achieves competitive performance both in terms of model-based and model-free indicators. Supplementary materials for this article are available online.
Databáze: OpenAIRE
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