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Testing under what conditions a product satisfies the desired properties is a fundamental problem in manufacturing industry. #link# 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 is