# High Dimensional Level Set Estimation with Bayesian Neural Network

arXiv: https://arxiv.org/abs/2012.09973 · HTML: https://mlsanity.com/paper/2012.09973/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [Nearly Optimal Algorithms for Level Set Estimation](https://mlsanity.com/paper/2111.01768/) (2021)
- [Black-box Few-shot Knowledge Distillation](https://mlsanity.com/paper/2207.12106/) (2022)
- [Active Level Set Estimation for Continuous Search Space with Theoretical Guarantee](https://mlsanity.com/paper/2402.16237/) (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)

## Abstract (arXiv)

Level Set Estimation (LSE) is an important problem with applications in various fields such as material design, biotechnology, machine operational testing, etc. Existing techniques suffer from the scalability issue, that is, these methods do not work well with high dimensional inputs. This paper proposes novel methods to solve the high dimensional LSE problems using Bayesian Neural Networks. In particular, we consider two types of LSE problems: (1) textitexplicit LSE problem where the threshold level is a fixed user-specified value, and, (2) textitimplicit LSE problem where the threshold level is defined as a percentage of the (unknown) maximum of the objective function. For each problem, we derive the corresponding theoretic information based acquisition function to sample the data points so as to maximally increase the level set accuracy. Furthermore, we also analyse the theoretical time complexity of our proposed acquisition functions, and suggest a practical methodology to efficiently tune the network hyper-parameters to achieve high model accuracy. Numerical experiments on both synthetic and real-world datasets show that our proposed method can achieve better results compared to existing state-of-the-art approaches.