# Adaptive Design of Experiments for Conservative Estimation of Excursion Sets

arXiv: https://arxiv.org/abs/1611.07256 · HTML: https://mlsanity.com/paper/1611.07256/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2016.

## Built on by (most cited first, 10 of 10)

- [Nearly Optimal Algorithms for Level Set Estimation](https://mlsanity.com/paper/2111.01768/) (2021)
- [Triangulation candidates for Bayesian optimization](https://mlsanity.com/paper/2112.07457/) (2021)
- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [Instance-Dependent Bounds for Zeroth-order Lipschitz Optimization with Error Certificates](https://mlsanity.com/paper/2102.01977/) (2021)
- [Look-Ahead Acquisition Functions for Bernoulli Level Set Estimation](https://mlsanity.com/paper/2203.09751/) (2022)
- [Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors](https://mlsanity.com/paper/2109.03457/) (2021)
- [Bayesian sequential design of computer experiments for quantile set inversion](https://mlsanity.com/paper/2211.01008/) (2022)
- [CRPS-Based Targeted Sequential Design with Application in Chemical Space](https://mlsanity.com/paper/2503.11250/) (2025)
- [A Finite-Horizon Approach to Active Level Set Estimation](https://mlsanity.com/paper/2310.11985/) (2023)
- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)

## Abstract (arXiv)

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, i.e. 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 formulae 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.