Testing under what conditions a 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, many issues remain to be solved for their practical use. As one of such issues, we consider the case where the input conditions cannot be controlled precisely—LSE problems under input uncertainty. We introduce a basic framework for handling input uncertainty in LSE problems 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 their applicability and effectiveness.

中文翻译：

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输入不确定性下水平集估计的主动学习及其扩展

在什么条件下测试产品满足所需特性是制造业中的一个基本问题。如果将条件和属性分别视为黑盒函数的输入和输出，则该任务可以解释为称为水平集估计（LSE）的问题：识别输入区域使得函数值是高于（或低于）阈值。尽管已经开发了各种解决 LSE 问题的方法，但在实际应用中仍有许多问题需要解决。作为此类问题之一，我们考虑无法精确控制输入条件的情况——输入不确定性下的 LSE 问题。我们介绍了处理 LSE 问题中输入不确定性的基本框架，然后提出具有适当理论保证的有效方法。所提出的方法和理论可以普遍应用于在输入不确定性下与 LSE 相关的各种挑战，例如成本相关输入不确定性和未知输入不确定性。我们将所提出的方法应用于人工和真实数据，以证明其适用性和有效性。