• 한국수학사학회지
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• 제35권1호
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• pp.1-18
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• 2022

This paper presents a statistical machine learning method that generates the implied volatility surface under the rareness of the market data. We apply the practitioner's Black-Scholes model and Gaussian process regression method to construct a Bayesian inference system with observed volatilities as a prior information and estimate the posterior distribution of the unobserved volatilities. The variance instead of the volatility is the target of the estimation, and the radial basis function is applied to the mean and kernel function of the Gaussian process regression. We present two types of Gaussian process regression methods and empirically analyze them.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권8호
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• pp.4285-4299
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• 2019

Adversarial attack is a technique that causes a malfunction of classification models by adding noise that cannot be distinguished by humans, which poses a threat to a deep learning model. In this paper, we propose an efficient method to detect adversarial images using Gaussian process regression. Existing deep learning-based adversarial detection methods require numerous adversarial images for their training. The proposed method overcomes this problem by performing classification based on the statistical features of adversarial images and clean images that are extracted by Gaussian process regression with a small number of images. This technique can determine whether the input image is an adversarial image by applying Gaussian process regression based on the intermediate output value of the classification model. Experimental results show that the proposed method achieves higher detection performance than the other deep learning-based adversarial detection methods for powerful attacks. In particular, the Gaussian process regression-based detector shows better detection performance than the baseline models for most attacks in the case with fewer adversarial examples.

• 로봇학회논문지
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• 제17권3호
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• pp.296-302
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• 2022

This paper proposes a center of plantar foot pressure (CoP) trajectory estimation method based on Gaussian process regression, with the aim to show robust results regardless of the regions and numbers of FSRs of the insole sensor. This method can bring an interpolation between the measurement points inside the wearable insole sensor, and two experiments are conducted for performance evaluation. For this purpose, the input data used in the experiment are generated in three types (13 FSRs, 8 FSRs, 5 FSRs) according to the regions and numbers of FSRs. First, the estimation results of the CoP trajectory are compared using Gaussian process regression and weighted mean. As a result of each method, the estimation results of the two methods were similar in the case of 13 FSRs data. On the other hand, in the case of the 8 and 5 FSRs data, the weighted mean varies depending on the regions and numbers of FSRs, but the estimation results of Gaussian process regression showed similar results in spite of reducing the regions and numbers. Second, the estimation results of the CoP trajectory based on Gaussian process regression during several gait cycles are analyzed. In five gait cycles, the previous cycle and the current estimation results are compared, and it was confirmed that similar trajectories appeared in all. In this way, the method of estimating the CoP trajectory based on Gaussian process regression showed robust results, and stability was confirmed by yielding similar results in several gait cycles.

• 응용통계연구
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• 제26권3호
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• pp.389-399
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• 2013

본 연구에서는 가우시안 과정회귀방법을 소개하고 시계열 마이크로어레이 유전자 발현데이터에 대해 가우시안 과정회귀를 적용한 사례를 보이고자한다. 가우시안 과정회귀를 적합하여 로그 주변우도함수 비를 이용한 유전자를 선별방법에 대한 모의실험을 통해 민감도, 특이도, 위발견율 등을 계산하여 선별방법으로의 활용성을 보였다. 실제 효모세포주기 데이터에 대해 제곱지수공분산함수를 고려한 가우시안 과정회귀를 적합하여 로그 주변우도함수 비를 이용하여 차변화된 유전자를 선별한 후, 선별된 유전자들에 대해 가우시안 모형기반 군집화를 하고 실루엣 값으로 군집유효성을 보였다.

• 반도체디스플레이기술학회지
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• 제11권3호
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• pp.19-25
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• 2012

The accuracy of Shape From Focus (SFF) technique depends on the quality of the focus measurements which are computed through a focus measure operator. In this paper, we introduce a new approach to estimate 3D shape of an object based on Gaussian process regression. First, initial depth is estimated by applying a conventional focus measure on image sequence and maximizing it in the optical direction. In second step, input feature vectors consisting of eginvalues are computed from 3D neighborhood around the initial depth. Finally, by utilizing these features, a latent function is developed through Gaussian process regression to estimate accurate depth. The proposed approach takes advantages of the multivariate statistical features and covariance function. The proposed method is tested by using image sequences of various objects. Experimental results demonstrate the efficacy of the proposed scheme.

• 한국정보과학회논문지:소프트웨어및응용
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• 제35권7호
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• pp.417-423
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• 2008

본 논문에서는 각 음원이 시간적 구조를 가졌을 경우 음원들을 분리해내는 확률적 음원분리 방법을 제안한다. 이를 위해 각 음원의 시간적 구조를 가우시안 프로세스(Gaussian process)로 모델링하고 기존의 음원분리 문제를 유사-가능도 최대화 문제(pseudo-likelihood maximization)로 공식화한다. 본 알고리즘을 통해 얻어진 데이타의 유사-가능도는 정규 분포이며 이는 가우시안 프로세스 회귀방법(Gaussian process regression)을 통해 쉽게 계산이 가능하다. 음원분리의 역혼합 행렬은 경도(gradient) 기반최적화 기법을 통해 데이타의 유사-가능도를 최대화하는 해를 찾음으로써 구해진다. 여러 실험을 통하여 제안 알고리듬이 몇 가지 특정 상황에서 기존의 분리 알고리듬들에 비해 우수한 성능을 보임을 확인 할 수 있다.

• Nuclear Engineering and Technology
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• 제52권8호
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• pp.1807-1816
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• 2020

In this work, a Gaussian Process (Kriging) approach is proposed to provide efficient dose mapping for complex radiation fields using limited number of responses. Given a few response measurements (or simulation data points), the proposed approach can help the analyst in completing a map of the radiation dose field with a 95% confidence interval, efficiently. Two case studies are used to validate the proposed approach. The First case study is based on experimental dose measurements to build the dose map in a radiation field induced by a D-D neutron generator. The second, is a simulation case study where the proposed approach is used to mimic Monte Carlo dose predictions in the radiation field using a limited number of MCNP simulations. Given the low computational cost of constructing Gaussian Process (GP) models, results indicate that the GP model can reasonably map the dose in the radiation field given a limited number of data measurements. Both case studies are performed on the nuclear engineering radiation laboratories at the University of Sharjah.

• Communications for Statistical Applications and Methods
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• 제24권4호
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• pp.383-396
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• 2017

The model in our approach assumes that computer responses are a realization of a Gaussian processes superimposed on a regression model called a Gaussian process regression model (GPRM). Selecting a subset of variables or building a good reduced model in classical regression is an important process to identify variables influential to responses and for further analysis such as prediction or classification. One reason to select some variables in the prediction aspect is to prevent the over-fitting or under-fitting to data. The same reasoning and approach can be applicable to GPRM. However, only a few works on the variable selection in GPRM were done. In this paper, we propose a new algorithm to build a good prediction model among some GPRMs. It is a post-work of the algorithm that includes the Welch method suggested by previous researchers. The proposed algorithms select some non-zero regression coefficients (${\beta}^{\prime}s$) using forward and backward methods along with the Lasso guided approach. During this process, the fixed were covariance parameters (${\theta}^{\prime}s$) that were pre-selected by the Welch algorithm. We illustrated the superiority of our proposed models over the Welch method and non-selection models using four test functions and one real data example. Future extensions are also discussed.

• Geomechanics and Engineering
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• 제34권5호
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• pp.507-527
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• 2023

Accurately estimation of the geo-mechanical parameters in Artificial Ground Freezing (AGF) is a most important scientific topic in soil improvement and geotechnical engineering. In order for this, one way is using classical and conventional constitutive models based on different theories like critical state theory, Hooke's law, and so on, which are time-consuming, costly, and troublous. The others are the application of artificial intelligence (AI) techniques to predict considered parameters and behaviors accurately. This study presents a comprehensive data-mining-based model for predicting the Young's Modulus of frozen sand under the triaxial test. For this aim, several single and hybrid models were considered including additive regression, bagging, M5-Rules, M5P, random forests (RF), support vector regression (SVR), locally weighted linear (LWL), gaussian process regression (GPR), and multi-layered perceptron neural network (MLP). In the present study, cell pressure, strain rate, temperature, time, and strain were considered as the input variables, where the Young's Modulus was recognized as target. The results showed that all selected single and hybrid predicting models have acceptable agreement with measured experimental results. Especially, hybrid Additive Regression-Gaussian Process Regression and Bagging-Gaussian Process Regression have the best accuracy based on Model performance assessment criteria.

• 대한원격탐사학회지
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• 제38권4호
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• pp.327-341
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• 2022

Cloud removal is often required to construct time-series sets of optical images for environmental monitoring. In regression-based cloud removal, the selection of an appropriate regression model and the impact analysis of the input images significantly affect the prediction performance. This study evaluates the potential of Gaussian process (GP) regression for cloud removal and also analyzes the effects of cloud-free optical images and spectral bands on prediction performance. Unlike other machine learning-based regression models, GP regression provides uncertainty information and automatically optimizes hyperparameters. An experiment using Sentinel-2 multi-spectral images was conducted for cloud removal in the two agricultural regions. The prediction performance of GP regression was compared with that of random forest (RF) regression. Various combinations of input images and multi-spectral bands were considered for quantitative evaluations. The experimental results showed that using multi-temporal images with multi-spectral bands as inputs achieved the best prediction accuracy. Highly correlated adjacent multi-spectral bands and temporally correlated multi-temporal images resulted in an improved prediction accuracy. The prediction performance of GP regression was significantly improved in predicting the near-infrared band compared to that of RF regression. Estimating the distribution function of input data in GP regression could reflect the variations in the considered spectral band with a broader range. In particular, GP regression was superior to RF regression for reproducing structural patterns at both sites in terms of structural similarity. In addition, uncertainty information provided by GP regression showed a reasonable similarity to prediction errors for some sub-areas, indicating that uncertainty estimates may be used to measure the prediction result quality. These findings suggest that GP regression could be beneficial for cloud removal and optical image reconstruction. In addition, the impact analysis results of the input images provide guidelines for selecting optimal images for regression-based cloud removal.