• Communications for Statistical Applications and Methods
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• 제25권5호
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• pp.453-470
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• 2018

We study how to distinguish the parameters of the sparse autoregressive (AR) process from zero using a non-convex penalized estimation. A class of non-convex penalties are considered that include the smoothly clipped absolute deviation and minimax concave penalties as special examples. We prove that the penalized estimators achieve some standard theoretical properties such as weak and strong oracle properties which have been proved in sparse linear regression framework. The results hold when the maximal order of the AR process increases to infinity and the minimal size of true non-zero parameters decreases toward zero as the sample size increases. Further, we construct a practical method to select tuning parameters using generalized information criterion, of which the minimizer asymptotically recovers the best theoretical non-penalized estimator of the sparse AR process. Simulation studies are given to confirm the theoretical results.

• Communications for Statistical Applications and Methods
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• 제27권6호
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• pp.603-624
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• 2020

There is an emerging interest in brain functional connectivity (FC) based on functional Magnetic Resonance Imaging in Alzheimer's disease (AD) studies. The complex and high-dimensional structure of FC makes it challenging to explore the association between altered connectivity and AD susceptibility. We develop a pipeline to refine FC as proper covariates in a penalized logistic regression model and classify normal and AD susceptible groups. Three different quantification methods are proposed for FC refinement. One of the methods is dimension reduction based on common component analysis (CCA), which is employed to address the limitations of the other methods. We applied the proposed pipeline to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data and deduced pathogenic FC biomarkers associated with AD susceptibility. The refined FC biomarkers were related to brain regions for cognition, stimuli processing, and sensorimotor skills. We also demonstrated that a model using CCA performed better than others in terms of classification performance and goodness-of-fit.

• Genomics & Informatics
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• 제14권4호
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• pp.149-159
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• 2016

With the success of the genome-wide association studies (GWASs), many candidate loci for complex human diseases have been reported in the GWAS catalog. Recently, many disease prediction models based on penalized regression or statistical learning methods were proposed using candidate causal variants from significant single-nucleotide polymorphisms of GWASs. However, there have been only a few systematic studies comparing existing methods. In this study, we first constructed risk prediction models, such as stepwise linear regression (SLR), least absolute shrinkage and selection operator (LASSO), and Elastic-Net (EN), using a GWAS chip and GWAS catalog. We then compared the prediction accuracy by calculating the mean square error (MSE) value on data from the Korea Association Resource (KARE) with body mass index. Our results show that SLR provides a smaller MSE value than the other methods, while the numbers of selected variables in each model were similar.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.1003-1011
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• 2008

Mixed-effect Poisson regression models are widely used for analysis of correlated count data such as those found in longitudinal studies. In this paper, we consider kernel extensions with semiparametric fixed effects and parametric random effects. The estimation is through the penalized likelihood method based on kernel trick and our focus is on the efficient computation and the effective hyperparameter selection. For the selection of hyperparameters, cross-validation techniques are employed. Examples illustrating usage and features of the proposed method are provided.

• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.129-140
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• 2020

In this paper, we introduce an efficient algorithm for the non-convex penalized multinomial logistic regression that can be uniformly applied to a class of non-convex penalties. The class includes most non-convex penalties such as the smoothly clipped absolute deviation, minimax concave and bridge penalties. The algorithm is developed based on the concave-convex procedure and modified local quadratic approximation algorithm. However, usual quadratic approximation may slow down computational speed since the dimension of the Hessian matrix depends on the number of categories of the output variable. For this issue, we use a uniform bound of the Hessian matrix in the quadratic approximation. The algorithm is available from the R package ncpen developed by the authors. Numerical studies via simulations and real data sets are provided for illustration.

• Journal of the Korean Data and Information Science Society
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• 제27권3호
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• pp.827-833
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• 2016

In this paper, we propose a deep least squares support vector machine (LS-SVM) for regression problems, which consists of the input layer and the hidden layer. In the hidden layer, LS-SVMs are trained with the original input variables and the perturbed responses. For the final output, the main LS-SVM is trained with the outputs from LS-SVMs of the hidden layer as input variables and the original responses. In contrast to the multilayer neural network (MNN), LS-SVMs in the deep LS-SVM are trained to minimize the penalized objective function. Thus, the learning dynamics of the deep LS-SVM are entirely different from MNN in which all weights and biases are trained to minimize one final error function. When compared to MNN approaches, the deep LS-SVM does not make use of any combination weights, but trains all LS-SVMs in the architecture. Experimental results from real datasets illustrate that the deep LS-SVM significantly outperforms state of the art machine learning methods on regression problems.

• 응용통계연구
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• 제22권1호
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• pp.115-127
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• 2009

The purpose of statistical analyses of array-CGH experiment data is to divide the whole genome into regions of equal copy number, to quantify the copy number in each region and finally to evaluate its significance of being different from two. Several statistical procedures have been proposed which include the circular binary segmentation, and a Gaussian based local regression for detecting break points (GLAD) by estimating a piecewise constant function. We propose in this note a penalized spline regression and its simultaneous confidence band(SCB) approach to evaluate the statistical significance of regions of genetic gain/loss. The region of which the simultaneous confidence band stays above 0 or below 0 can be considered as a region of genetic gain or loss. We compare the performance of the SCB procedure with GLAD and hidden Markov model approaches through a simulation study in which the data were generated from AR(1) and AR(2) models to reflect spatial dependence of the array-CGH data in addition to the independence model. We found that the SCB method is more sensitive in detecting the low level copy number alterations.

• Communications for Statistical Applications and Methods
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• 제28권1호
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• pp.21-37
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• 2021

There is a direct connection between linear discriminant analysis (LDA) and linear regression since the direction vector of the LDA can be obtained by the least square estimation. The connection motivates the penalized LDA when the model is high-dimensional where the number of predictive variables is larger than the sample size. In this paper, we study the penalized LDA for a class of penalties, called the moderately clipped LASSO (MCL), which interpolates between the least absolute shrinkage and selection operator (LASSO) and minimax concave penalty. We prove that the MCL penalized LDA correctly identifies the sparsity of the Bayes direction vector with probability tending to one, which is supported by better finite sample performance than LASSO based on concrete numerical studies.

• Communications for Statistical Applications and Methods
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• 제29권6호
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• pp.641-653
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• 2022

Penalized least squares methods are important tools to simultaneously select variables and estimate parameters in linear regression. The penalized maximum likelihood can also be used for the same purpose assuming that the error distribution falls in a certain parametric family of distributions. However, the use of a certain parametric family can suffer a misspecification problem which undermines the estimation accuracy. To give sufficient flexibility to the error distribution, we propose to use the symmetric log-concave error distribution with LASSO penalty. A feasible algorithm to estimate both nonparametric and parametric components in the proposed model is provided. Some numerical studies are also presented showing that the proposed method produces more efficient estimators than some existing methods with similar variable selection performance.

• Journal of the Korean Data and Information Science Society
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• 제20권6호
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• pp.1093-1101
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• 2009

분위수 회귀모형은 확률변수들 사이에 확률적인 관계구조를 포함한 함수 모형을 좀 더 완벽하게 추정하도록 제공한다. 본 논문에서는 함수 추정에 로버스트하다고 알려져 있는 서포트벡터기계 기법과 이중벌칙커널기계를 이용하여 분위수 회귀모형을 추정하고자 한다. 이중벌칙커널기계는 고차원의 입력변수에 대한 분위수 회귀가 요구될 때 분위수 회귀모형을 잘 추정한다고 알려져 있다. 또한 본 논문에서는 광범위한 형태의 분위수 회귀모형 추정을 위해서 정규분포보다 비대칭 라플라스 분포를 이용한다. 본 논문에서 제안한 모형은 분위수 회귀모형 추정을 위해서 서포트벡터기계 기법에 이중벌칙커널기계를 이용하여 각각의 평균과 분산을 동시에 추정한다. 평균과 분산함수 추정을 위해 사용된 커널함수의 모수들은 최적의 값을 찾기 위해 일반화근사 교차타당성을 이용한다.