• The Korean Journal of Applied Statistics
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• v.34 no.1
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• pp.9-23
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• 2021

In the following paper we introduce a variational Bayes method that approximates posterior distributions with mean-field method. In particular, we introduce automatic differentiation variation inference (ADVI), which approximates joint posterior distributions using the product of Gaussian distributions after transforming parameters into real coordinate space, and then apply it to pharmacokinetic models that are models for the study of the time course of drug absorption, distribution, metabolism and excretion. We analyze real data sets using ADVI and compare the results with those based on Markov chain Monte Carlo. We implement the algorithms using Stan.

• The Korean Journal of Applied Statistics
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• v.35 no.3
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• pp.445-455
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• 2022

In this paper, we introduce existing Bayesian methods for high-dimensional sparse regression models and compare their performance in various simulation scenarios. Especially, we focus on the variational Bayes approach proposed by Ray and Szabó (2021), which enables scalable and accurate Bayesian inference. Based on simulated data sets from sparse high-dimensional linear regression models, we compare the variational Bayes approach with other Bayesian and frequentist methods. To check the practical performance of the variational Bayes in logistic regression models, a real data analysis is conducted using leukemia data set.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.5
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• pp.1249-1254
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• 2008

The crucial part of graphical model is to compute the posterior distribution of parameters plus with the hidden variables given the observed data. In this paper, implementation of variational Bayes method for Gaussian mixture model and derivation of factorial variational approximation have been proposed. This result can be used for data analysis tasks like information retrieval or data visualization.

• The Korean Journal of Applied Statistics
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• v.36 no.2
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• pp.115-127
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• 2023

Multinomial probit model is a popular model for multiclass classification and choice model. Markov chain Monte Carlo (MCMC) method is widely used for estimating multinomial probit model, but its computational cost is high. However, it is well known that variational Bayesian approximation is more computationally efficient than MCMC, because it uses subsets of samples. In this study, we describe multinomial probit model with Gaussian process classification and how to employ variational Bayesian approximation on the model. This study also compares the results of variational Bayesian multinomial probit model to the results of naive Bayes, K-nearest neighbors and support vector machine for the UCI mice protein expression level data.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.2
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• pp.159-171
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• 2001

평면 아치 구조물에 대해 선형 탄성 변분방정식에 기반을 둔 설계민감도 해석을 위한 일반적 이론을 개발하였다. 아치 구조물내의 임의 마디에 정의된 응력범함수를 고려하였고 이에 대한 설계민감도 공식을 유도하기 위해 전미분(material derivative) 개념과 보조(adjoint) 변수 방법을 도입하였다. 얻어진 민감도 공식은 구조해석 결과를 얻고 나면 이들로부터 단순 대수연산을 통해 계산이 되므로 적용이 간편할 뿐 아니라 해의 정확도가 높은 잇점이 있다. 본 방법은 아치의 형상을 매개변수를 통해 표현하므로 얕은 아치에 국한하지 않고 어떠한 형상도 고려가 가능하며, 나아가서 아치의 형상변화를 형상에 대해 수직뿐 아니라 접선방향도 포함하여 일반적으로 고려하므로 다양한 형상설계가 가능하다. 몇 가지 예제에서 민감도 계산을 수행함으로써 본 방법의 정확도와 효율성을 입증하였으며, 두 가지의 설계최적화 문제를 대상으로 실제로 두께 및 형상최적설계를 수행하였다.

• Journal of KIISE:Computing Practices and Letters
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• v.14 no.5
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• pp.527-531
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• 2008

For statistical modeling, the model parameters are usually estimated by maximizing a probability measure, such as the likelihood or the posterior. In contrast, a variational Bayesian method treats the parameters of a model as probability distributions and computes optimal distributions for them rather than values. It has been shown that this approach effectively avoids the overfitting problem, which is common with other parameter optimization methods. This paper applies a variational Bayesian technique to surface fitting for height field data. Then, we propose point cloud denoising based on the basic surface fitting technique. Validation experiments and further tests with scan data verify the robustness of the proposed method.

• Honam Mathematical Journal
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• v.3 no.1
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• pp.167-173
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• 1981

본(本) 논문(論文)은 M. S. Robertson이 만든 함수족(函數族) G(0, 2)에 대(對)한 변분공식(變分公式)(1, 3)을 확장하여 함수족(函數族) $G(\alpha, k)$, $$(\mid\alpha\mid<\frac{\pi}{2},\;k{\geq_-}2)$$에 적용이 되는 새 변분공식(變分公式) (2.18)을 유도하고, 그것을 증명하였다. 그 증명과정(證明過程)은 Schiffer나 Hummel의 방법(方法)을 사용(使用)하지 않고, Poisson-Stieltijes 적분공식(積分公式)을 이용(利用)하여 새로운 방법(方法)으로 증명하는 데 성공(成功)하였다.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.251-267
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• 2015

The Indian Buffet Process is a stochastic process on equivalence classes of binary matrices having finite rows and infinite columns. The Indian Buffet Process can be imposed as the prior distribution on the binary matrix in an infinite feature model. We describe the derivation of the Indian buffet process from a finite feature model, and briefly explain the relation between the Indian buffet process and the beta process. Using a Gaussian linear model, we describe three algorithms: Gibbs sampling algorithm, Stick-breaking algorithm and variational method, with application for finding features in image data. We also illustrate the use of the Indian Buffet Process in various type of analysis such as dyadic data analysis, network data analysis and independent component analysis.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07b
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• pp.619-621
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• 2005

은닉 마코프 모델은 이산 동역학을 표현할 수 있는 확률 모형이다. 우도 함수 최적화를 수행하는 전통적인 Baum-Welch 학습 알고리즘은 국소해로 수령하기 쉬우며, 우도함수의 특성상 복잡한 모델을 선호하는 바이어스가 존재한다. 베이지안 프레임워크에서는 파라미터를 랜덤 변수로 보고 이에 대한 사후 확률 분포를 추정하여 이 문제를 해결할 수 있다. 본 논문에서는 베이지안 추정을 위한 결정론적 근사화 기법인 변분 베이지안 방법을 이용, 출력 노드에 가우시안 혼합 노드를 지니는 일반화된 HMM의 추론 방법을 유도한다. 인공 데이터에 대한 실험을 통해, 본 방법이 효과적인 HMM 학습을 수행할 수 있음을 보인다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.944-951
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• 1988

Global-Local Laminate Variational Model is utilized to investigate the characteristics of interlaminar stresses in thick composite laminates under uniform axial extension. Various laminates with different fiber orientation and stacking sequences are analyzed to observe the behavior of interlaminar normal stresses. From this result, the interlaminar normal stress distribution along the laminate interfaces is examined and discussed with an existing approximation model. The repeated stacking of Poisson's ratio symmetric sublaminates is found to be the best stacking method of thick composite laminates to reduce the interlaminar normal stresses for the prevention of the free-edge delamination.