# Active learning for level set estimation under input uncertainty and its extensions

arXiv: https://arxiv.org/abs/1909.06064 · HTML: https://mlsanity.com/paper/1909.06064/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2019.

## Built on by (most cited first, 7 of 7)

- [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)
- [Few-shot Algorithm Assurance](https://mlsanity.com/paper/2412.20275/) (2024)
- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)

## Abstract (arXiv)

Testing under what conditions the product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function, this task can be interpreted as the problem called Level Set Estimation (LSE) -- the problem of identifying input regions such that the function value is above (or below) a threshold. Although various methods for LSE problems have been developed so far, there are still many issues to be solved for their practical usage. As one of such issues, we consider the case where the input conditions cannot be controlled precisely, i.e., LSE problems under input uncertainty. We introduce a basic framework for handling input uncertainty in LSE problem, and then propose efficient methods with proper theoretical guarantees. The proposed methods and theories can be generally applied to a variety of challenges related to LSE under input uncertainty such as cost-dependent input uncertainties and unknown input uncertainties. We apply the proposed methods to artificial and real data to demonstrate the applicability and effectiveness.