# Bayesian Experimental Design for Finding Reliable Level Set under Input Uncertainty

arXiv: https://arxiv.org/abs/1910.12043 · HTML: https://mlsanity.com/paper/1910.12043/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2019.

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

- [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)
- [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)
- [Efficient Determination of Safety Requirements for Perception Systems](https://mlsanity.com/paper/2307.01371/) (2023)
- [Multi-Metric Adaptive Experimental Design Under a Fixed Budget with Validation](https://mlsanity.com/paper/2506.03062/) (2025)
- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)
- [Multi-Objective Coverage via Constraint Active Search](https://mlsanity.com/paper/2602.15595/) (2026)

## Abstract (arXiv)

In the manufacturing industry, it is often necessary to repeat expensive operational testing of machine in order to identify the range of input conditions under which the machine operates properly. Since it is often difficult to accurately control the input conditions during the actual usage of the machine, there is a need to guarantee the performance of the machine after properly incorporating the possible variation in input conditions. In this paper, we formulate this practical manufacturing scenario as an Input Uncertain Reliable Level Set Estimation (IU-rLSE) problem, and provide an efficient algorithm for solving it. The goal of IU-rLSE is to identify the input range in which the outputs smaller/greater than a desired threshold can be obtained with high probability when the input uncertainty is properly taken into consideration. We propose an active learning method to solve the IU-rLSE problem efficiently, theoretically analyze its accuracy and convergence, and illustrate its empirical performance through numerical experiments on artificial and real data.