Jooyong Shim

Varying coefficient modeling via least squares support vector regression

The varying coefficient regression model has received a great deal of attention as an important tool for modeling the dynamic changes of regression coefficients in the social and natural sciences. Lots of efforts have been devoted to develop effective estimation methods for such regression model. In this paper we propose a method for fitting the varying coefficient regression model using the least squares support vector regression technique, which analyzes the dynamic relation between a response and a group of covariates. We also consider a generalized cross validation method for choosing the hyperparameters which affect the performance of the proposed method. We provide a method for estimating the confidence intervals of coefficient functions. The proposed method is evaluated through simulation and real example studies.

Semiparametric spatial effects kernel minimum squared error model for predicting housing sales prices

Semiparametric regression models have been extensively used to predict housing sales prices, but semiparametric kernel machines with spatial effect have not been studied yet. This paper proposes the semiparametric spatial effect kernel minimum squared error model (SSEKMSEM) and the semiparametric spatial effect least squares support vector machine (SSELS-SVM) for estimating a hedonic price function and compares the price prediction performance with the conventional parametric models and a semiparametric generalized additive model (GAM). This paper utilizes two data sets. One is a large data set representing 5966 single-family residential home sales between July 2000 and August 2008 from Pitt County, North Carolina. The other is a data set of residential property sales records from September 2000 to September 2004 in Carteret County, North Carolina. The results show that the SSEKMSEM and SSELS-SVM outperform the parametric counterparts and the semiparametric GAM in both in-sample and out-of-sample price predictions, indicating that these kernel machines can be useful for measurement and prediction of housing sales prices.

Semiparametric mixed-effect least squares support vector machine for analyzing pharmacokinetic and pharmacodynamic data

In this paper we propose a semiparametric mixed-effect least squares support vector machine (LS-SVM) regression model for the analysis of pharmacokinetic (PK) and pharmacodynamic (PD) data. We also develop the generalized cross-validation (GCV) method for choosing the hyperparameters which affect the performance of the proposed LS-SVM. The performance of the proposed LS-SVM is compared with those of NONMEM and the regular semiparametric LS-SVM via four measures, which are mean squared error (MSE), mean absolute error (MAE), mean relative absolute error (MRAE) and mean relative prediction error (MRPE). Through paired-t test statistic we find that the absolute values of four measures of the proposed LS-SVM are significantly smaller than those of NONMEM for PK and PD data. We also investigate the coefficient of determinations R^2s of predicted and observed values. The R^2s of NONMEM are 0.66 and 0.59 for PK and PD data, respectively, while the R^2s of the proposed LS-SVM are 0.94 and 0.96. Through cross validation technique we also find that the proposed LS-SVM shows better generalization performance than the regular semiparametric LS-SVM for PK and PD data. These facts indicate that the proposed LS-SVM is an appealing tool for analyzing PK and PD data.

Semivarying coefficient least-squares support vector regression for analyzing high-dimensional gene-environmental data

ABSTRACT In the context of genetics and genomic medicine, gene-environment (G×E) interactions have a great impact on the risk of human diseases. Some existing methods for identifying G×E interactions are considered to be limited, since they analyze one or a few number of G factors at a time, assume linear effects of E factors, and use inefficient selection methods. In this paper, we propose a new method to identify significant main effects and G×E interactions. This is based on a semivarying coefficient least-squares support vector regression (LS-SVR) technique, which is devised by utilizing flexible semiparametric LS-SVR approach for censored survival data. This semivarying coefficient model is used to deal with the nonlinear effects of E factors. We also derive a generalized cross validation (GCV) function for determining the optimal values of hyperparameters of the proposed method. This GCV function is also used to identify significant main effects and G×E interactions. The proposed method is evaluated through numerical studies.

Transcription factor-binding site identification and gene classification via fusion of the supervised-weighted discrete kernel clustering and support vector machine

The genetic regulatory mechanism heavily influences a substantial portion of biological functions and processes needed to sustain life. For a comprehensive mechanistic understanding of biological processes, it is important to identify the common transcription factor (TF) binding sites (TFBSs) from a set of promoter sequences of co-regulated genes and classify genes that are co-regulated by certain TFs, therefore to provide an insight into the mechanism that underlies the interaction among the co-regulated genes and complicate genetic regulation. We propose a new supervised-weighted discrete kernel clustering (SWDKC) classification method for the identification of TFBS and the classification of gene. Our SWDKC method gave smaller misclassification error rate than the other methods on both the simulated data and the real NF-κB data. We verify that the selected over-represented TFBSs serve informative TFBSs from a biological point of view.

Kernel-based random effect time-varying coefficient model for longitudinal data

Abstract Lots of efforts have been devoted to develop effective estimation methods for parametric and nonparametric longitudinal data models. Varying coefficient regression model has received a great deal of attention as an important tool for modeling the relation between a response and a group of predictor variables. The varying coefficient model is particularly useful in longitudinal data analysis. A random effect time-varying coefficient model is proposed for analyzing longitudinal data, which is based on the basic principle of least squares support vector machine along with the kernel technique. A generalized cross validation method is also considered for choosing the tolerance level and the hyperparameters which affect the performance of the proposed model. The proposed model is evaluated through numerical studies.

Monotone support vector quantile regression

ABSTRACT Quantile regression (QR) models have received a great deal of attention in both the theoretical and applied statistical literature. In this paper we propose support vector quantile regression (SVQR) with monotonicity restriction, which is easily obtained via the dual formulation of the optimization problem. We also provide the generalized approximate cross validation method for choosing the hyperparameters which affect the performance of the proposed SVQR. The experimental results for the synthetic and real data sets confirm the successful performance of the proposed model.

Estimating small area mean with mixed and fixed effects support vector median regressions

Abstract Small area estimation has been extensively studied under linear mixed effects models. However, when the functional form of the relationship between the response and the covariates is not linear, it may lead to biased estimators of the small area parameters. In this paper, we relax the assumption of linear regression for the fixed part of the model and replace it by using the underlying concept of support vector quantile regression. This makes it possible to express the nonparametric small area estimation problem as mixed or fixed effects model regression. Through numerical studies we compare the efficiency of different models in estimating small area mean.