arXiv subjects

Yu Inatsu

Publications and source records attributed to Yu Inatsu.

24 records · Page 2Linked to original sources

arXiv2021

Active learning for distributionally robust level-set estimation

Many cases exist in which a black-box function $f$ with high evaluation cost depends on two types of variables $\bm x$ and $\bm w$, where $\bm x$ is a controllable \emph{design} variable and $\bm w$ are uncontrollable \emph{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 $\bm x$ such that the function $f(\bm x, \bm w)$ has the desired properties by incorporating the random variation of the environmental variables $\bm w$. A natural measure of robustness is the probability that $f(\bm x, \bm w)$ exceeds a given threshold $h$, which is known as the \emph{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 \textit{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.

stat.ML↗

arXiv2020

Mean-Variance Analysis in Bayesian Optimization under Uncertainty

We consider active learning (AL) in an uncertain environment in which trade-off between multiple risk measures need to be considered. As an AL problem in such an uncertain environment, we study Mean-Variance Analysis in Bayesian Optimization (MVA-BO) setting. Mean-variance analysis was developed in the field of financial engineering and has been used to make decisions that take into account the trade-off between the average and variance of investment uncertainty. In this paper, we specifically focus on BO setting with an uncertain component and consider multi-task, multi-objective, and constrained optimization scenarios for the mean-variance trade-off of the uncertain component. When the target blackbox function is modeled by Gaussian Process (GP), we derive the bounds of the two risk measures and propose AL algorithm for each of the above three problems based on the risk measure bounds. We show the effectiveness of the proposed AL algorithms through theoretical analysis and numerical experiments.

stat.ML↗

arXiv2020

Bayesian Quadrature Optimization for Probability Threshold Robustness Measure

In many product development problems, the performance of the product is governed by two types of parameters called design parameter and environmental parameter. While the former is fully controllable, the latter varies depending on the environment in which the product is used. The challenge of such a problem is to find the design parameter that maximizes the probability that the performance of the product will meet the desired requisite level given the variation of the environmental parameter. In this paper, we formulate this practical problem as active learning (AL) problems and propose efficient algorithms with theoretically guaranteed performance. Our basic idea is to use Gaussian Process (GP) model as the surrogate model of the product development process, and then to formulate our AL problems as Bayesian Quadrature Optimization problems for probabilistic threshold robustness (PTR) measure. We derive credible intervals for the PTR measure and propose AL algorithms for the optimization and level set estimation of the PTR measure. We clarify the theoretical properties of the proposed algorithms and demonstrate their efficiency in both synthetic and real-world product development problems.

stat.ML↗

arXiv2019

Computing Valid p-values for Image Segmentation by Selective Inference

Image segmentation is one of the most fundamental tasks of computer vision. In many practical applications, it is essential to properly evaluate the reliability of individual segmentation results. In this study, we propose a novel framework to provide the statistical significance of segmentation results in the form of p-values. Specifically, we consider a statistical hypothesis test for determining the difference between the object and the background regions. This problem is challenging because the difference can be deceptively large (called segmentation bias) due to the adaptation of the segmentation algorithm to the data. To overcome this difficulty, we introduce a statistical approach called selective inference, and develop a framework to compute valid p-values in which the segmentation bias is properly accounted for. Although the proposed framework is potentially applicable to various segmentation algorithms, we focus in this paper on graph cut-based and threshold-based segmentation algorithms, and develop two specific methods to compute valid p-values for the segmentation results obtained by these algorithms. We prove the theoretical validity of these two methods and demonstrate their practicality by applying them to segmentation problems for medical images.

cs.CV↗

arXiv2019

Bayesian Experimental Design for Finding Reliable Level Set under Input Uncertainty

In the manufacturing industry, it is often necessary to repeat expensive operational testing of machine in order to identify the range of input conditions under which the machine operates properly. Since it is often difficult to accurately control the input conditions during the actual usage of the machine, there is a need to guarantee the performance of the machine after properly incorporating the possible variation in input conditions. In this paper, we formulate this practical manufacturing scenario as an Input Uncertain Reliable Level Set Estimation (IU-rLSE) problem, and provide an efficient algorithm for solving it. The goal of IU-rLSE is to identify the input range in which the outputs smaller/greater than a desired threshold can be obtained with high probability when the input uncertainty is properly taken into consideration. We propose an active learning method to solve the IU-rLSE problem efficiently, theoretically analyze its accuracy and convergence, and illustrate its empirical performance through numerical experiments on artificial and real data.

stat.ML↗

arXiv2019

Active learning for enumerating local minima based on Gaussian process derivatives

We study active learning (AL) based on Gaussian Processes (GPs) for efficiently enumerating all of the local minimum solutions of a black-box function. This problem is challenging due to the fact that local solutions are characterized by their zero gradient and positive-definite Hessian properties, but those derivatives cannot be directly observed. We propose a new AL method in which the input points are sequentially selected such that the confidence intervals of the GP derivatives are effectively updated for enumerating local minimum solutions. We theoretically analyze the proposed method and demonstrate its usefulness through numerical experiments.

stat.ML↗