Active learning for level set estimation under input uncertainty and its extensions
This addresses a practical issue in manufacturing and related fields for identifying input regions that meet desired output thresholds despite uncertain conditions, though it appears incremental in extending existing LSE approaches.
The paper tackles the problem of Level Set Estimation (LSE) under input uncertainty, where input conditions cannot be precisely controlled, by introducing a framework and proposing efficient methods with theoretical guarantees. The methods are applied to artificial and real data to demonstrate effectiveness.
Testing under what conditions the product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function, this task can be interpreted as the problem called Level Set Estimation (LSE) -- the problem of identifying input regions such that the function value is above (or below) a threshold. Although various methods for LSE problems have been developed so far, there are still many issues to be solved for their practical usage. As one of such issues, we consider the case where the input conditions cannot be controlled precisely, i.e., LSE problems under input uncertainty. We introduce a basic framework for handling input uncertainty in LSE problem, and then propose efficient methods with proper theoretical guarantees. The proposed methods and theories can be generally applied to a variety of challenges related to LSE under input uncertainty such as cost-dependent input uncertainties and unknown input uncertainties. We apply the proposed methods to artificial and real data to demonstrate the applicability and effectiveness.