Bayesian Active Learning of (small) Quantile Sets through Expected Estimator Modification

Given a multivariate function taking deterministic and unc ertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs f or which the probability that the output belongs to a specific region remains below a given threshold. To solve this problem in the context of expensive-to-evaluate black-box functions, we propose a Bayesian active learning strategy based on Gaussian process modeling. The strategy is driven by a nov el sampling criterion, which belongs to a broader principle that we refer to as Expected Estimator Modification (EEM). More specifically, the strategy relies on a novel sampling criterion combined w ith a sequential Monte Carlo framework that enables the construction of batch-sequential designs for the efficient estimation of small quantile sets. The performance of the strategy is illustrated on seve ral synthetic examples and an industrial application case involving the ROTOR37 compressor model.