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

Giang Ngo, Dat Phan Trong, Dang Nguyen, Sunil Gupta
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1315-1323, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-ngo26a, title = { High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions }, author = {Ngo, Giang and Trong, Dat Phan and Nguyen, Dang and Gupta, Sunil}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1315--1323}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/ngo26a/ngo26a.pdf}, url = {https://proceedings.mlr.press/v300/ngo26a.html}, 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. } }
Endnote
%0 Conference Paper %T High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions %A Giang Ngo %A Dat Phan Trong %A Dang Nguyen %A Sunil Gupta %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-ngo26a %I PMLR %P 1315--1323 %U https://proceedings.mlr.press/v300/ngo26a.html %V 300 %X 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.
APA
Ngo, G., Trong, D.P., Nguyen, D. & Gupta, S.. (2026). High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1315-1323 Available from https://proceedings.mlr.press/v300/ngo26a.html.

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