High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions

Giang Ngo, Dat Phan Trong, Dang Nguyen, Sunil Gupta

Abstract:

Level set estimation (LSE) classifies whether an unknown function's value exceeds a specified threshold for given inputs, a fundamental problem in many real-world applications.
In active learning settings with limited initial data, we aim to iteratively acquire informative points to construct an accurate classifier for this task.
In high-dimensional spaces, this becomes challenging where the search volume grows exponentially with increasing dimensionality.
We propose TRLSE, an algorithm for high-dimensional LSE, which identifies and refines regions near the threshold boundary with dual acquisition functions operating at both global and local levels.
We provide a theoretical analysis of TRLSE's accuracy and show its superior sample efficiency against existing methods through extensive evaluations on multiple synthetic and real-world LSE problems.

Submission Number: 590