# Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation

arXiv: https://arxiv.org/abs/1807.06712 · HTML: https://mlsanity.com/paper/1807.06712/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2018.

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

- [Entropy-based adaptive design for contour finding and estimating reliability](https://mlsanity.com/paper/2105.11357/) (2021)
- [Look-Ahead Acquisition Functions for Bernoulli Level Set Estimation](https://mlsanity.com/paper/2203.09751/) (2022)
- [Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes](https://mlsanity.com/paper/2407.09739/) (2024)
- [Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC](https://mlsanity.com/paper/2104.03942/) (2021)
- [Practical Bayesian Algorithm Execution via Posterior Sampling](https://mlsanity.com/paper/2410.20596/) (2024)
- [Stochastic Cell Transmission Models of Traffic Networks](https://mlsanity.com/paper/2304.11654/) (2023)
- [Gearing Gaussian process modeling and sequential design towards stochastic simulators](https://mlsanity.com/paper/2412.07306/) (2024)
- [Non-Myopic Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2412.08085/) (2024)
- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)
- [Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions](https://mlsanity.com/paper/2504.20527/) (2025)

## Abstract (arXiv)

We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic samplers, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-t observations; (ii) Student-t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1--6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.