High Dimensional Level Set Estimation with Bayesian Neural Network
This work provides a solution for the scalability issue in high-dimensional Level Set Estimation, which is crucial for applications in material design, biotechnology, and machine operational testing.
This paper addresses the challenge of high-dimensional Level Set Estimation (LSE) by proposing novel methods using Bayesian Neural Networks. The approach tackles both explicit and implicit LSE problems, demonstrating superior performance compared to existing state-of-the-art methods on synthetic and real-world datasets.
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) \textit{explicit} LSE problem where the threshold level is a fixed user-specified value, and, (2) \textit{implicit} 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.