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

TL;DR

This paper introduces a Bayesian active learning method using Gaussian processes and a novel sampling criterion, EEM, to efficiently estimate small quantile sets in expensive black-box functions, demonstrated on synthetic and industrial examples.

Contribution

It proposes a new sampling criterion, EEM, combined with a sequential Monte Carlo framework for batch-sequential design in quantile set estimation.

Findings

Effective in synthetic examples

Successful application to industrial case

Improves efficiency of quantile set estimation

Abstract

Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for 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 novel 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 with 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 several synthetic examples and an industrial application case involving the ROTOR37 compressor model.