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

arXiv: https://arxiv.org/abs/2506.13211 · HTML: https://mlsanity.com/paper/2506.13211/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 61 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 6 of 6)

- [A supermartingale approach to Gaussian process based sequential design of experiments](https://mlsanity.com/paper/1608.01118/) (2016)
- [Global Sensitivity Analysis with Dependence Measures](https://mlsanity.com/paper/1311.2483/) (2013)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [The ICSCREAM methodology: Identification of penalizing configurations in computer experiments using screening and metamodel -- Applications in thermal-hydraulics](https://mlsanity.com/paper/2004.04663/) (2020)
- [Bayesian sequential design of computer experiments for quantile set inversion](https://mlsanity.com/paper/2211.01008/) (2022)
- [Consistency of some sequential experimental design strategies for excursion set estimation based on vector-valued Gaussian processes](https://mlsanity.com/paper/2310.07315/) (2023)

## Abstract (arXiv)

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.