# Robust Super-Level Set Estimation using Gaussian Processes

arXiv: https://arxiv.org/abs/1811.09977 · HTML: https://mlsanity.com/paper/1811.09977/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2018.

## Built on by (most cited first, 15 of 15)

- [Nearly Optimal Algorithms for Level Set Estimation](https://mlsanity.com/paper/2111.01768/) (2021)
- [Active learning for distributionally robust level-set estimation](https://mlsanity.com/paper/2102.04000/) (2021)
- [Look-Ahead Acquisition Functions for Bernoulli Level Set Estimation](https://mlsanity.com/paper/2203.09751/) (2022)
- [Bayesian Optimization for Distributionally Robust Chance-constrained Problem](https://mlsanity.com/paper/2201.13112/) (2022)
- [Adaptive Defective Area Identification in Material Surface Using Active Transfer Learning-based Level Set Estimation](https://mlsanity.com/paper/2304.01404/) (2023)
- [Active Level Set Estimation for Continuous Search Space with Theoretical Guarantee](https://mlsanity.com/paper/2402.16237/) (2024)
- [Active Learning for Level Set Estimation Using Randomized Straddle Algorithms](https://mlsanity.com/paper/2408.03144/) (2024)
- [Optimal subgroup selection](https://mlsanity.com/paper/2109.01077/) (2021)
- [Practical Bayesian Algorithm Execution via Posterior Sampling](https://mlsanity.com/paper/2410.20596/) (2024)
- [Efficient Determination of Safety Requirements for Perception Systems](https://mlsanity.com/paper/2307.01371/) (2023)
- [Robust Transfer Learning for Active Level Set Estimation with Locally Adaptive Gaussian Process Prior](https://mlsanity.com/paper/2410.05660/) (2024)
- [Multi-Metric Adaptive Experimental Design Under a Fixed Budget with Validation](https://mlsanity.com/paper/2506.03062/) (2025)
- [High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions](https://mlsanity.com/paper/2602.12391/) (2026)
- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)
- [Online Adaptive Kernel Mixing for Gaussian Process Decision Making](https://mlsanity.com/paper/2609.19891/) (2026)

## Abstract (arXiv)

This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that function evaluations are costly. To select the next query point, we propose maximizing the expected volume of the domain identified as above the threshold as predicted by a Gaussian process, robustified by a variance term. We also give asymptotic guarantees on the exploration effect of the algorithm, regardless of the prior misspecification. We show by various numerical examples that our approach also outperforms existing techniques in the literature in practice.