Published In
Foundations of Data Science
Document Type
Pre-Print
Publication Date
11-1-2024
Subjects
Mathematics
Abstract
We consider the problem of active learning for level set estimation (LSE), where the goal is to localize all regions where a function of interest lies above/below a given threshold as quickly as possible. We present a finitehorizon search procedure to perform LSE in one dimension while optimally balancing both the final estimation error and the distance traveled during active learning for a fixed number of samples. A tuning parameter is used to trade off between the estimation accuracy and distance traveled. We show that the resulting optimization problem can be solved in closed form and that the resulting policy generalizes existing approaches to this problem. We then show how this approach can be used to perform level set estimation in two dimensions, under some additional assumptions, under the popular Gaussian process model. Empirical results on synthetic data indicate that as the cost of travel increases, our method’s ability to treat distance nonmyopically allows it to significantly improve on the state of the art. On real air quality data, our approach achieves roughly oy one fifth the estimation error at less than half the cost of competing algorithms.
Rights
© Copyright the author(s) 2024
Locate the Document
DOI
10.3934/fods.2024050
Persistent Identifier
https://archives.pdx.edu/ds/psu/42887
Citation Details
Kearns, P., Jedynak, B., & Lipor, J. (2024). A finite-horizon approach to active level set estimation. Foundations of Data Science, 0(0), 0–0.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: A finite-horizon approach to active level set estimation. Foundations of Data Science, 0(0), 0–0.