  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.
