Active Learning for Enumerating Local Minima Based on Gaussian Process Derivatives

Yu, I.; Sugita, Daisuke; Toyoura, Kazuaki; Takeuchi, Ichiro

doi:10.1162/neco_a_01307

Cited by 4 publications

(2 citation statements)

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“…Several studies have been conducted on active learning for LSE [4,8,30,10]. Furthermore, some researchers applied LSE to efficiently identify safety regions [25,27,24,28], and others used LSE to enumerate the local minima of black-box functions [9].…”

Section: Related Workmentioning

confidence: 99%

Active learning for distributionally robust level-set estimation

Inatsu,

Iwazaki,

Takeuchi

2021

Preprint

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Many cases exist in which a black-box function f with high evaluation cost depends on two types of variables x and w, where x is a controllable design variable and w are uncontrollable environmental variables that have random variation following a certain distribution P . In such cases, an important task is to find the range of design variables x such that the function f (x, w) has the desired properties by incorporating the random variation of the environmental variables w. A natural measure of robustness is the probability that f (x, w) exceeds a given threshold h, which is known as the probability threshold robustness (PTR) measure in the literature on robust optimization. However, this robustness measure cannot be correctly evaluated when the distribution P is unknown. In this study, we addressed this problem by considering the distributionally robust PTR (DRPTR) measure, which considers the worst-case PTR within given candidate distributions. Specifically, we studied the problem of efficiently identifying a reliable set H, which is defined as a region in which the DRPTR measure exceeds a certain desired probability α, which can be interpreted as a level set estimation (LSE) problem for DRPTR. We propose a theoretically grounded and computationally efficient active learning method for this problem. We show that the proposed method has theoretical guarantees on convergence and accuracy, and confirmed through numerical experiments that the proposed method outperforms existing methods.

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Section: Related Workmentioning

confidence: 99%

Active learning for distributionally robust level-set estimation

Inatsu,

Iwazaki,

Takeuchi

2021

Preprint

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“…Here, bioengineers need to identify the level set (the region in the protein feature space in which the protein satisfies the required functional properties) by repeatedly modifying amino acid sequences of proteins. Various extensions of LSE problem have also been recently studied (Inatsu, Karasuyama, Inoue, Kandori, & Takeuchi, 2020;Inatsu, Sugita, Toyoura, & Takeuchi, 2020).…”

Section: Introductionmentioning

confidence: 99%

Active Learning for Level Set Estimation Under Input Uncertainty and Its Extensions

Karasuyama

Inoue

et al. 2020

Neural Computation

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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.

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